Journal articles: 'Invariance principles (Physics)'

1

Moldoveanu, Florin. "Quantum mechanics from invariance principles." Journal of Physics: Conference Series 626 (July 3, 2015): 012067. http://dx.doi.org/10.1088/1742-6596/626/1/012067.

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Connor, J. W. "Invariance principles and plasma confinement." Plasma Physics and Controlled Fusion 30, no. 6 (June 1, 1988): 619–50. http://dx.doi.org/10.1088/0741-3335/30/6/001.

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Manno, Gianni, Juha Pohjanpelto, and Raffaele Vitolo. "Gauge invariance, charge conservation, and variational principles." Journal of Geometry and Physics 58, no. 8 (August 2008): 996–1006. http://dx.doi.org/10.1016/j.geomphys.2008.03.006.

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Grigore, D. R. "The derivation of Einstein equations from invariance principles." Classical and Quantum Gravity 9, no. 6 (June 1, 1992): 1555–71. http://dx.doi.org/10.1088/0264-9381/9/6/012.

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Arunasalam, V. "Are the invariance principles really truly Lorentz-covariant?" Foundations of Physics Letters 7, no. 6 (December 1994): 515–30. http://dx.doi.org/10.1007/bf02219747.

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Mathieu, P. "Quenched Invariance Principles for Random Walks with Random Conductances." Journal of Statistical Physics 130, no. 5 (November 28, 2007): 1025–46. http://dx.doi.org/10.1007/s10955-007-9465-z.

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Roychowdhury, Dibakar. "Broken Lifshitz Invariance, Spin Waves, and Hydrodynamics." Advances in High Energy Physics 2019 (June 2, 2019): 1–12. http://dx.doi.org/10.1155/2019/5356121.

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In this paper, based on the basic principles of thermodynamics, we explore the hydrodynamic regime of interacting Lifshitz field theories in the presence of broken rotational invariance. We compute the entropy current and discover new dissipative effects which are consistent with the principle of local entropy production in the fluid. In our analysis, we consider both the parity even and the parity odd sector upto first order in the derivative expansion. Finally, we argue that the present construction of the paper could be systematically identified as that of the hydrodynamic description associated with spin waves (away from the domain of quantum criticality) under certain limiting conditions.

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Ryckman, Thomas. "Invariance Principles as Regulative Ideals: From Wigner to Hilbert." Royal Institute of Philosophy Supplement 63 (October 2008): 63–80. http://dx.doi.org/10.1017/s1358246108000040.

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Eugene Wigner's several general discussions of symmetry and invariance principles are among the canonical texts of contemporary philosophy of physics. Wigner spoke from a position of authority, having pioneered (and won the Nobel prize in 1963) for recognition of the importance of symmetry principles from nuclear to molecular physics. But perhaps recent commentators have not sufficiently stressed that Wigner always took care to situate the notion of invariance principles with respect to two others, initial conditions (or events) and laws of nature. Wigner's first such general consideration of invariance principles, an address presented at Einstein's 70th birthday celebration, held in Princeton on 19 March 1949, began by laying out just this distinction, and in a way that seems to suggest that the three notions arise through abstraction in an analysis of the general problem of cognition in the natural sciences: The world is very complicated and it is clearly impossible for the human mind to understand it completely. Man has therefore devised an artifice which permits the complicated nature of the world to be blamed on something which is called accidental and thus permits him to abstract a domain in which simple laws can be found. The complications are called initial conditions; the domain of regularities, laws of nature. (…) the underlying abstraction is probably one of the most fruitful the human mind has made. It has made the natural sciences possible.

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Grigore, D. R. "A derivation of the Nambu-Goto action from invariance principles." Journal of Physics A: Mathematical and General 25, no. 13 (July 7, 1992): 3797–811. http://dx.doi.org/10.1088/0305-4470/25/13/026.

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Stanley, H. E., L. A. N. Amaral, P. Gopikrishnan, P. Ch Ivanov, T. H. Keitt, and V. Plerou. "Scale invariance and universality: organizing principles in complex systems." Physica A: Statistical Mechanics and its Applications 281, no. 1-4 (June 2000): 60–68. http://dx.doi.org/10.1016/s0378-4371(00)00195-3.

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Kreinovich, Vladik. "Astronomical tests of relativity: beyond parameterized post-Newtonian formalism (PPN), to testing fundamental principles." Proceedings of the International Astronomical Union 5, S261 (April 2009): 56–61. http://dx.doi.org/10.1017/s1743921309990159.

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AbstractBy the early 1970s, the improved accuracy of astrometric and time measurements enabled researchers not only to experimentally compare relativistic gravity with the Newtonian predictions, but also to compare different relativistic gravitational theories (e.g., the Brans-Dicke Scalar-Tensor Theory of Gravitation). For this comparison, Kip Thorne and others developed the Parameterized Post-Newtonian Formalism (PPN), and derived the dependence of different astronomically observable effects on the values of the corresponding parameters.Since then, all the observations have confirmed General Relativity. In other words, the question of which relativistic gravitation theory is in the best accordance with the experiments has been largely settled. This does not mean that General Relativity is the final theory of gravitation: it needs to be reconciled with quantum physics (into quantum gravity), it may also need to be reconciled with numerous surprising cosmological observations, etc. It is, therefore, reasonable to prepare an extended version of the PPN formalism, that will enable us to test possible quantum-related modifications of General Relativity.In particular, we need to include the possibility of violating fundamental principles that underlie the PPN formalism but that may be violated in quantum physics, such as scale-invariance, T-invariance, P-invariance, energy conservation, spatial isotropy violations, etc. In this paper, we present the first attempt to design the corresponding extended PPN formalism, with the (partial) analysis of the relation between the corresponding fundamental physical principles.

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Mathieu, P., and A. Piatnitski. "Quenched invariance principles for random walks on percolation clusters." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2085 (July 3, 2007): 2287–307. http://dx.doi.org/10.1098/rspa.2007.1876.

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We consider a supercritical Bernoulli percolation model in , d ≥2, and study the simple symmetric random walk on the infinite percolation cluster. The aim of this paper is to prove the almost sure (quenched) invariance principle for this random walk.

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Falmagne, Jean-Claude. "Meaningfulness and Order-Invariance: Two Fundamental Principles for Scientific Laws." Foundations of Physics 34, no. 9 (September 2004): 1341–84. http://dx.doi.org/10.1023/b:foop.0000044096.50863.8e.

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Ganapol, B. D. "Solution to the linear BGK equation via the principles of invariance." Journal of Physics A: Mathematical and General 29, no. 6 (March 21, 1996): 1227–44. http://dx.doi.org/10.1088/0305-4470/29/6/010.

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15

Reis, A. Heitor. "Constructal Theory: From Engineering to Physics, and How Flow Systems Develop Shape and Structure." Applied Mechanics Reviews 59, no. 5 (September 1, 2006): 269–82. http://dx.doi.org/10.1115/1.2204075.

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Constructal theory and its applications to various fields ranging from engineering to natural living and inanimate systems, and to social organization and economics, are reviewed in this paper. The constructal law states that if a system has freedom to morph it develops in time the flow architecture that provides easier access to the currents that flow through it. It is shown how constructal theory provides a unifying picture for the development of flow architectures in systems with internal flows (e.g., mass, heat, electricity, goods, and people). Early and recent works on constructal theory by various authors covering the fields of heat and mass transfer in engineered systems, inanimate flow structures (river basins, global circulations) living structures, social organization, and economics are reviewed. The relation between the constructal law and the thermodynamic optimization method of entropy generation minimization is outlined. The constructal law is a self-standing principle, which is distinct from the Second Law of Thermodynamics. The place of the constructal law among other fundamental principles, such as the Second Law, the principle of least action and the principles of symmetry and invariance is also presented. The review ends with the epistemological and philosophical implications of the constructal law.

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Melbourne, Ian, and Andrei Török. "Central Limit Theorems and Invariance Principles¶for Time-One Maps of Hyperbolic Flows." Communications in Mathematical Physics 229, no. 1 (August 2002): 57–71. http://dx.doi.org/10.1007/s00220-002-0676-5.

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Krupka, Demeter. "Invariant variational structures on fibered manifolds." International Journal of Geometric Methods in Modern Physics 12, no. 02 (January 29, 2015): 1550020. http://dx.doi.org/10.1142/s0219887815500206.

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The aim of this paper is to present a relatively complete theory of invariance of global, higher-order integral variational functionals in fibered spaces, as developed during a few past decades. We unify and extend recent results of the geometric invariance theory; new results on deformations of extremals are also included. We show that the theory can be developed by means of the general concept of invariance of a differential form in geometry, which does not require different ad hoc modifications. The concept applies to invariance of Lagrangians, source forms and Euler–Lagrange forms, as well as to extremals of the given variational functional. Equations for generators of invariance transformations of the Lagrangians and the Euler–Lagrange forms are characterized in terms of Lie derivatives. As a consequence of invariance, we derive the global Noether's theorem on existence of conserved currents along extremals, and discuss the meaning of conservation equations. We prove a theorem describing extremals, whose deformations by a vector field are again extremals. The general settings and structures we use admit extension of the global invariance theory to variational principles in physics, especially in field theory.

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PESTIEAU, J., C. SMITH, and S. TRINE. "POSITRONIUM DECAY: GAUGE INVARIANCE AND ANALYTICITY." International Journal of Modern Physics A 17, no. 10 (April 20, 2002): 1355–98. http://dx.doi.org/10.1142/s0217751x02009606.

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The construction of positronium decay amplitudes is handled through the use of dispersion relations. In this way, emphasis is put on basic QED principles: gauge invariance and soft-photon limits (analyticity).A firm grounding is given to the factorization approaches, and some ambiguities in the spin and energy structures of the positronium wave function are removed. Nonfactorizable amplitudes are naturally introduced. Their dynamics are described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness of the present theoretical predictions for the decay rates is then addressed. Indeed, some of those nonfactorizable contributions are unaccounted for by NRQED analyses. However, it is shown that such new contributions are highly suppressed, being of [Formula: see text].Finally, a particular effective form factor formalism is constructed for parapositronium, allowing a thorough analysis of binding energy effects and analyticity implementation.

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Debbasch, Fabrice. "Action principles for quantum automata and Lorentz invariance of discrete time quantum walks." Annals of Physics 405 (June 2019): 340–64. http://dx.doi.org/10.1016/j.aop.2019.03.005.

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20

CLINE, DAVID B. "TEST OF FUNDAMENTAL SYMMETRY PRINCIPLES AT A ϕ FACTORY." Modern Physics Letters A 07, no. 26 (August 30, 1992): 2351–68. http://dx.doi.org/10.1142/s0217732392003785.

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We describe the tests of various symmetry principles at a ϕ factory. The most important new tests will be for the validity of CPT invariance at an extremely sensitive level. We indicate the current level of model independent limitation on CPT violation. Tests of new gravity interactions as well as CP violation in various K decays are described as well as some interest in new probes of quantum mechanics. A brief description of the Frascati, Novosibirsk and UCLA ϕ factory designs are also given.

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Hohmann, Manuel. "Variational Principles in Teleparallel Gravity Theories." Universe 7, no. 5 (April 21, 2021): 114. http://dx.doi.org/10.3390/universe7050114.

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We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that, in addition to the tetrad or metric, they employ a flat connection as additional field variable, but dthey iffer by the presence of absence of torsion and nonmetricity for this independent connection. Besides the different underlying geometric formulation using a tetrad or metric as fundamental field variable, one has different choices to introduce the conditions of vanishing curvature, torsion, and nonmetricity, either by imposing them a priori and correspondingly restricting the variation of the action when the field equations are derived, or by using Lagrange multipliers. Special care must be taken, since these conditions form non-holonomic constraints. Here, we explicitly show that all of the aforementioned approaches are equivalent, and that the same set of field equations is obtained, independently of the choice of the geometric formulation and variation procedure. We further discuss the consequences arising from the diffeomorphism invariance of the gravitational action, and show how they establish relations between the gravitational field equations.

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22

Aste, Andreas. "Perturbative quantum gauge invariance: where the ghosts come from." Canadian Journal of Physics 83, no. 2 (February 1, 2005): 139–63. http://dx.doi.org/10.1139/p04-064.

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A condensed introduction to quantum gauge theories is given in the perturbative S-matrix framework, with path-integral methods used nowhere. This approach emphasizes the fact that it is not necessary to start from classical gauge theories that are then subject to quantization: it is possible, instead, to recover the classical group structure and coupling properties from purely quantum-mechanical principles. As a main tool, we use a free-field version of the BecchiRouetStoraTyutin gauge transformation, which contains no interaction terms related to a coupling constant. This free gauge transformation can be formulated in an analogous way for quantum electrodynamics, YangMills theories with massless or massive gauge bosons, and quantum gravity. PACS Nos.: 11.10.z, 11.15.Bt, 12.20.Ds, 12.38.Bx

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HSU, JONG-PING, and DANA FINE. "THE DEVELOPMENT OF THE GRAVITATIONAL AND YANG–MILLS FIELDS, AND THE TREATMENT OF ACCELERATED FRAMES." International Journal of Modern Physics A 20, no. 32 (December 30, 2005): 7485–504. http://dx.doi.org/10.1142/s0217751x05025255.

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We discuss ideas and problems regarding classical and quantum gravity, gauge theory of gravity, and space–time transformations between accelerated frames. Both Einstein's theory of gravity and Yang–Mills theory are gauge invariant. The invariance principles are at the very heart of our understanding of the physical world. This paper attempts to survey the development and to reveal problems and limitations of various formulations to gravitational and Yang–Mills fields, and to space–time transformations of accelerated frames. Gravitational force and accelerated frames are two ingredients in Einstein's thought in the period around 1907. Accelerated frames are difficult to define and are not well developed. However, one cannot claim to have a complete understanding of the physical world, if one understands flat space–time physics only from the viewpoint of the special class of inertial frames and ignores the vast class of noninertial frames. The paper highlights three aspects: (1) ideas of gravity as a Yang–Mills field, first discussed by Utiyama; (2) problems of quantum gravity, discussed by Feynman, Dyson and others; (3) space–time properties and the physics of fields and particles in accelerated frames of reference. These unfulfilled aspects of Einstein and Yang–Mills' profound thoughts present a challenge to physicists and mathematicians in the 21st century.

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Ipek, Selman, and Ariel Caticha. "The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity." Symmetry 12, no. 8 (August 7, 2020): 1324. http://dx.doi.org/10.3390/sym12081324.

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Entropic dynamics (ED) are a general framework for constructing indeterministic dynamical models based on entropic methods. ED have been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum scalar field propagating in dynamical space-time. The approach rests on a few key ingredients: (1) Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. (2) In accordance with the standard entropic methods of inference, the dynamics are dictated by information encoded in constraints. (3) The choice of the physically relevant constraints is dictated by principles of symmetry and invariance. The first of such principle imposes the preservation of a symplectic structure which leads to a Hamiltonian formalism with its attendant Poisson brackets and action principle. The second symmetry principle is foliation invariance, which, following earlier work by Hojman, Kuchař, and Teitelboim, is implemented as a requirement of path independence. The result is a hybrid ED model that approaches quantum field theory in one limit and classical general relativity in another, but is not fully described by either. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle.

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POPOVA, A. D., and A. N. PETROV. "NONLINEAR QUANTUM MECHANICS WITH NONCLASSICAL GRAVITATIONAL SELF-INTERACTION II: NONSTATIONARY SITUATION." International Journal of Modern Physics A 08, no. 16 (June 30, 1993): 2683–707. http://dx.doi.org/10.1142/s0217751x93001077.

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Quantum mechanics (first quantization) with self-consistent gravitational interaction, previously constructed for the stationary case, is extended to the general case. The two requirements for such a theory are realized: to obtain the theory maximally resembling a classical field theory and to achieve the invariance of the theory under the rescaling transformations of a wave function. The construction is not trivial, because it rejects the variational principles of extremality of any action and involves some principles of smoothed extremality which give relevant equations.

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Horváth, D. "Tests of the CPT Invariance at the Antiproton Decelerator of CERN." Ukrainian Journal of Physics 64, no. 7 (September 17, 2019): 589. http://dx.doi.org/10.15407/ujpe64.7.589.

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The Standard Model, the theory of particle physics is based on symmetries: both the structure of the composite particles and their interactions are derived using gauge invariance principles. Some of these are violated by the weak interaction like parity and CP symmetry, and even masses are created via spontaneous symmetry breaking. CPT invariance, the most essential symmetry of the Standard Model, states the equivalency of matter and antimatter. However, because of the lack of antimatter in our Universe it is continuously tested at CERN. We overview these experiments: measuring the properties of antiprotons as compared to those of the proton at the Antiproton Decelerator and also searching for antimatter in cosmic rays.

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Malin, Peter E., Peter C. Leary, Lawrence M. Cathles, and Christopher C. Barton. "Observational and Critical State Physics Descriptions of Long-Range Flow Structures." Geosciences 10, no. 2 (January 28, 2020): 50. http://dx.doi.org/10.3390/geosciences10020050.

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Using Fracture Seismic methods to map fluid-conducting fracture zones makes it important to understand fracture connectivity over distances greater 10–20 m in the Earth’s upper crust. The principles required for this understanding are developed here from the observations that (1) the spatial variations in crustal porosity are commonly associated with spatial variations in the magnitude of the natural logarithm of crustal permeability, and (2) many parameters, including permeability have a scale-invariant power law distribution in the crust. The first observation means that crustal permeability has a lognormal distribution that can be described as κ ≈ κ 0 exp ( α ( φ − φ 0 ) ) , where α is the ratio of the standard deviation of ln permeability from its mean to the standard deviation of porosity from its mean. The scale invariance of permeability indicates that αϕο = 3 to 4 and that the natural log of permeability has a 1/k pink noise spatial distribution. Combined, these conclusions mean that channelized flow in the upper crust is expected as the distance traversed by flow increases. Locating the most permeable channels using Seismic Fracture methods, while filling in the less permeable parts of the modeled volume with the correct pink noise spatial distribution of permeability, will produce much more realistic models of subsurface flow.

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Antoine, Jean-Pierre. "Group Theory: Mathematical Expression of Symmetry in Physics." Symmetry 13, no. 8 (July 26, 2021): 1354. http://dx.doi.org/10.3390/sym13081354.

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The present article reviews the multiple applications of group theory to the symmetry problems in physics. In classical physics, this concerns primarily relativity: Euclidean, Galilean, and Einsteinian (special). Going over to quantum mechanics, we first note that the basic principles imply that the state space of a quantum system has an intrinsic structure of pre-Hilbert space that one completes into a genuine Hilbert space. In this framework, the description of the invariance under a group G is based on a unitary representation of G. Next, we survey the various domains of application: atomic and molecular physics, quantum optics, signal and image processing, wavelets, internal symmetries, and approximate symmetries. Next, we discuss the extension to gauge theories, in particular, to the Standard Model of fundamental interactions. We conclude with some remarks about recent developments, including the application to braid groups.

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Bálint, Péter, and Ian Melbourne. "Decay of Correlations and Invariance Principles for Dispersing Billiards with Cusps, and Related Planar Billiard Flows." Journal of Statistical Physics 133, no. 3 (September 25, 2008): 435–47. http://dx.doi.org/10.1007/s10955-008-9623-y.

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SYROS, C. "PRINCIPLES OF A NEW QUANTUM THEORY." Modern Physics Letters A 13, no. 21 (July 10, 1998): 1675–88. http://dx.doi.org/10.1142/s0217732398001753.

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The principles of a random quantum theory (R-QT) which is alternatively time-asymmetric or time-symmetric if the quantization is Fermi–Dirac or Bose–Enstein, respectively are presented. Bohr's quantization rule is applied on the field-action integral. A time topological space, [Formula: see text], is mathematically defined in which the paradoxes in standard quantum theory are solved. The time "quantum", is created as a regular, positive into-map of an observed observable's change resulting from a fundamental interaction process. [Formula: see text] is constructed as the union of time elements and can be embedded disconnectedly in the continuous Newtonian universal time, [Formula: see text]. Six axioms are formulated characterizing the space–time and R-QT. The disconnectedness of the (κ×λκ)-fold time-space, [Formula: see text], imparts a kind of disconnectedness to the κ×λκ-fold space–times, [Formula: see text], and induces the chrono-topology. In chrono-topology the unitary, U, or non-measure preserving, R, dynamics, is implemented by means of a time evolution, "complex" operator, [Formula: see text]. It breaks down by means of Bohr quantization into: [Formula: see text][Formula: see text] coincides formally — apart from the spontaneous renormalization — with the time evolution operator in the standard QFT. [Formula: see text] is a novum and produces the Maxwell–Boltzmann energy level distribution in a non-Euclidean QFT. Compatibility between time-reversal invariance of the standard QT equations and irreversibility of some phenomena both in microcosmos and macrocosmos is obtained. The [Formula: see text]-evolution leads to a time's arrow on quantum-scale systems.

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Ni, Wei-Tou. "From Equivalence Principles to Cosmology: Cosmic Polarization Rotation, CMB Observation, Neutrino Number Asymmetry, Lorentz Invariance and CPT." Progress of Theoretical Physics Supplement 172 (2008): 49–60. http://dx.doi.org/10.1143/ptps.172.49.

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Tawfik, A., and A. Diab. "Generalized uncertainty principle: Approaches and applications." International Journal of Modern Physics D 23, no. 12 (October 2014): 1430025. http://dx.doi.org/10.1142/s0218271814300250.

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In this paper, we review some highlights from the String theory, the black hole physics and the doubly special relativity and some thought experiments which were suggested to probe the shortest distances and/or maximum momentum at the Planck scale. Furthermore, all models developed in order to implement the minimal length scale and/or the maximum momentum in different physical systems are analyzed and compared. They entered the literature as the generalized uncertainty principle (GUP) assuming modified dispersion relation, and therefore are allowed for a wide range of applications in estimating, for example, the inflationary parameters, Lorentz invariance violation, black hole thermodynamics, Saleker–Wigner inequalities, entropic nature of gravitational laws, Friedmann equations, minimal time measurement and thermodynamics of the high-energy collisions. One of the higher-order GUP approaches gives predictions for the minimal length uncertainty. A second one predicts a maximum momentum and a minimal length uncertainty, simultaneously. An extensive comparison between the different GUP approaches is summarized. We also discuss the GUP impacts on the equivalence principles including the universality of the gravitational redshift and the free fall and law of reciprocal action and on the kinetic energy of composite system. The existence of a minimal length and a maximum momentum accuracy is preferred by various physical observations. The concern about the compatibility with the equivalence principles, the universality of gravitational redshift and the free fall and law of reciprocal action should be addressed. We conclude that the value of the GUP parameters remain a puzzle to be verified.

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MILTON, KIMBALL A., and OLGA P. SOLOVTSOVA. "PERTURBATIVE EXPANSIONS IN THE INCLUSIVE DECAY OF THE TAU-LEPTON." International Journal of Modern Physics A 17, no. 26 (October 20, 2002): 3789–808. http://dx.doi.org/10.1142/s0217751x02010935.

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A comparative analysis is performed for various forms of perturbative expansions in spacelike and timelike regions. As applied to the inclusive decay of the τ-lepton, comparison is given for the results derived within the framework of the standard perturbation theory and the analytic approach that modernizes perturbative expansions so that the new approximations reflect basic principles of the theory: renormalization invariance, spectrality, and causality. Advantages and self-consistency of the analytic approach in describing τ-lepton decay are demonstrated.

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BOUDJEMA, F. "SUBSTRUCTURE EFFECTS AT LEP100." International Journal of Modern Physics A 06, no. 01 (January 10, 1991): 1–19. http://dx.doi.org/10.1142/s0217751x91000022.

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I briefly review the searches being performed at LEP100 for new particles and novel interactions in the context of a composite structure. While the emphasis is on the most promising signals, the presentation follows a very broad phenomenological approach rather than listing predictions from specific models of substructure although some general guiding principles (such as chiral symmetry and global SU(2) weak invariance) have been incorporated in the analysis. Preliminary limits on the masses of certain particles are set from the autumn 1989 run.

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GELLER, MICHAEL R. "EFFECTIVE FIELD THEORY OF SINGLE AND MULTILAYERED QUANTUM HALL FLUIDS." International Journal of Modern Physics B 08, no. 10 (April 30, 1994): 1375–90. http://dx.doi.org/10.1142/s0217979294000622.

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We review an effective field theory of the quantum Hall fluid, where electron currents are expressed in terms of multiple-component gauge fields, and develop further the case of two-component fields. The form of the effective action, a simple matrix Chern-Simons action, is dictated by the principles of current conservation, dimensional analysis, gauge invariance, and by the presence of a gap. The formalism naturally describes multiple-component systems such as coupled Hall fluids in layered geometries, in addition to describing more complicated single-fluid states. We provide a complete classification of fractional quantum Hall states describable by two-component Chern-Simons gauge fields.

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LAJKÓ, PÉTER. "RENORMALIZATION-GROUP INVESTIGATION OF THE S = 1 RANDOM ANTIFERROMAGNETIC HEISENBERG CHAIN." International Journal of Modern Physics C 17, no. 12 (December 2006): 1739–53. http://dx.doi.org/10.1142/s0129183106010169.

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We introduce variants of the Ma-Dasgupta renormalization-group (RG) approach for random quantum spin chains, in which the energy-scale is reduced by decimation built on either perturbative or non-perturbative principles. In one non-perturbative version of the method, we require the exact invariance of the lowest gaps, while in a second class of perturbative Ma-Dasgupta techniques, different decimation rules are utilized. For the S = 1 random antiferromagnetic Heisenberg chain, both type of methods provide the same type of disorder dependent phase diagram, which is in agreement with density-matrix renormalization-group calculations and previous studies.

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KIEU, T. D. "GAUGE-INVARIANT QUANTISATION OF CHIRAL GAUGE THEORIES." Modern Physics Letters A 05, no. 03 (January 30, 1990): 175–82. http://dx.doi.org/10.1142/s0217732390000214.

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The path-integral functional of chiral gauge theories with background gauge potentials are derived in the holomorphic representation. Justification is provided, from first quantum mechanical principles, for the appearance of a functional phase factor of the gauge fields in order to maintain the gauge invariance. This term is shown to originate either from the Berry phase of the first-quantized hamiltonians or from the normal ordering of the second-quantized hamiltonian with respect to the Dirac in-vacuum. The quantization of the chiral Schwinger model is taken as an example.

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COMELLAS, JORDI, PETER E. HAAGENSEN, and JOSÉ I. LATORRE. "DIFFERENTIAL RENORMALIZATION FOR CURVED SPACE AND FINITE TEMPERATURE." International Journal of Modern Physics A 10, no. 19 (July 30, 1995): 2819–39. http://dx.doi.org/10.1142/s0217751x95001339.

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We derive, based only on simple principles of renormalization in coordinate space, closed renormalized amplitudes and renormalization group constants at one- and two-loop orders for scalar field theories in general backgrounds. This is achieved through a renormalization procedure we develop exploiting the central idea behind differential renormalization, which needs as the only inputs the propagator and the appropriate Laplacian for the backgrounds in question. We work out this coordinate space renormalization in some detail, and subsequently back it up with specific calculations for scalar theories both on curved backgrounds, manifestly preserving diffeomorphism invariance, and at finite temperature.

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Bogdanovich, V. A., and A. G. Vostretsov. "Application of the invariance and robustness principles in the development of demodulation algorithms for wideband communications systems." Journal of Communications Technology and Electronics 54, no. 11 (November 2009): 1283–91. http://dx.doi.org/10.1134/s1064226909110072.

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VAN TONDER, ANDRÉ. "WORLDSHEET COVARIANT PATH INTEGRAL QUANTIZATION OF STRINGS." International Journal of Modern Physics A 21, no. 32 (December 30, 2006): 6525–74. http://dx.doi.org/10.1142/s0217751x0603446x.

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We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on noncovariant operator regularizations, interesting operators here are true tensor objects with classical transformation laws, even on target spaces where the theory has a Weyl anomaly. Since no implicit noncovariant gauge choices are involved in the definition of the operators, the anomaly is clearly separated from the issue of operator renormalization and can be understood in isolation, instead of infecting the latter as in other approaches. Our method is of wider applicability to covariant theories that are not Weyl invariant, but where covariant tensor operators are desired. After constructing covariantly regularized vertex operators, we define a class of background-independent path integral measures suitable for string quantization. We show how gauge invariance of the path integral implies the usual physical state conditions in a very conceptually clean way. We then discuss the construction of the BRST action from first principles, obtaining some interesting caveats relating to its general covariance. In our approach, the expected BRST related anomalies are encoded somewhat differently from other approaches. We conclude with an unusual but amusing derivation of the value D = 26 of the critical dimension.

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McCauley, Joseph L. "The new science of complexity." Discrete Dynamics in Nature and Society 1, no. 1 (1997): 17–30. http://dx.doi.org/10.1155/s1026022697000046.

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Deterministic chaos, and even maximum computational complexity, have been discovered within Newtonian dynamics. Economists assume that prices and price changes can also obey abstract mathematical laws of motion. Sociologists and other postmodernists advertise that physics and chemistry have outgrown their former limitations, that chaos and complexity provide new holistic paradigms for science, and that the boundaries between the hard and the soft sciences, once impenetrable, have disappeared like the Berlin Wall. Three hundred years after the deaths of Galileo, Descartes, and Kepler, and the birth of Newton, reductionism appears to be on the decline, with holistic approaches to science on the upswing. We therefore examine the evidence that dynamical laws of motion may be discovered from empirical studies of chaotic or complex phenomena, and also review the foundation of reductionism in invariance principles.

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Arima, Takashi, Tommaso Ruggeri, and Masaru Sugiyama. "Rational extended thermodynamics of dense polyatomic gases incorporating molecular rotation and vibration." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2170 (March 30, 2020): 20190176. http://dx.doi.org/10.1098/rsta.2019.0176.

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The paper aims to construct a rational extended thermodynamics (RET) theory of dense polyatomic gases by taking into account the experimental evidence that the relaxation time of molecular rotation and that of molecular vibration are quite different from each other. For simplicity, we focus on gases with only one dissipative process due to bulk viscosity. In fact, in some polyatomic gases, the effect of bulk viscosity is much larger than that of shear viscosity and heat conductivity. The present theory includes the previous RET theory of dense gases with six fields as a particular case, and it also includes the RET theory of rarefied polyatomic gases with seven fields in the rarefied-gas limit. The closure is carried out by using the universal principles, that is, Galilean invariance and objectivity, entropy principle, and thermodynamic stability (convexity of entropy), where the duality principle connecting rarefied gases to dense gases also plays an important role. A detailed discussion is devoted to the expression of the production terms in the system of balance equations. As typical examples, we study a gas with virial equations of state and a van der Waals gas. Lastly the dispersion relation of a linear wave is derived, and its comparison with experimental data is made. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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POPOVA, A. D., and A. N. PETROV. "NONLINEAR QUANTUM MECHANICS WITH NONCLASSICAL GRAVITATIONAL SELF-INTERACTION III: RELATED TOPICS." International Journal of Modern Physics A 08, no. 16 (June 30, 1993): 2709–34. http://dx.doi.org/10.1142/s0217751x93001089.

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Some problems are considered in the framework of general quantum mechanics with gravitational self-interaction constructed earlier. A number of them were analyzed for the stationary situation. Here, the problem of gauge invariance generated by translations which do not violate the 3 + 1 splitting is studied. The notions of position and momentum operators are extended to the general case. The uncertainty relations are obtained for the uncertainty of the Ricci tensor and for uncertainties of the position and momentum of a particle. The correspondence between the stationary and nonstationary cases is examined at the level of variational principles. At least, the one-particle and two-particle problems in the Newtonian–Schrödingerian limit are considered; the latter problem is compared with the standard two-particle quantum problem to demonstrate the advantage of our approach.

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Wang, Fan, W. M. Sun, X. S. Chen, and P. M. Zhang. "Gauge invariance, canonical quantization and Poincaré covariance in nucleon structure." International Journal of Modern Physics: Conference Series 29 (January 2014): 1460249. http://dx.doi.org/10.1142/s201019451460249x.

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There are different quark and gluon momentum, spin and orbital angular momentum operators used in the study of nucleon structure. We analyze the physical contents of these operators and propose a new set of operators based on gauge invariance principle, canonical quantization rule and Poincaré covariance. Atomic structure is a simpler testing ground of these operators and has been analyzed together. These new operators are the gauge invariant version of the gauge non-invariant canonical version used in physics since the establishment of quantum mechanics and reduce to the familiar canonical ones in Coulomb gauge.

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WU, YUE-LIANG. "SYMMETRY PRINCIPLE PRESERVING AND INFINITY FREE REGULARIZATION AND RENORMALIZATION OF QUANTUM FIELD THEORIES AND THE MASS GAP." International Journal of Modern Physics A 18, no. 29 (November 20, 2003): 5363–419. http://dx.doi.org/10.1142/s0217751x03015222.

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Through defining irreducible loop integrals (ILI's), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILI's are obtained to maintain the generalized Ward identities of gauge invariance in non-Abelian gauge theories. The ILI's of arbitrary loop graphs can be evaluated from the corresponding Feynman loop integrals by adopting an ultraviolet (UV) divergence preserving parameter method. Overlapping UV divergences are explicitly shown to be factorizable in the ILI's and be harmless via suitable subtractions. A new regularization and renormalization method is presented in the initial space–time dimension of the theory. The procedure respects unitarity and causality. Of interest, the method leads to an infinity free renormalization and meanwhile maintains the symmetry principles of the original theory except the intrinsic mass scale caused conformal scaling symmetry breaking and the anomaly induced symmetry breaking. Tadpole graphs of Yang–Mills gauge fields are found to play an essential role for maintaining manifest gauge invariance via cancellations of quadratically divergent ILI's. Quantum field theories (QFT's) regularized through the new method are well defined and governed by a physically meaningful characteristic energy scale (CES) Mc and a physically interesting sliding energy scale (SES) μs which can run from μs ~ Mc to a dynamically generated mass gap μs = μc or to μs = 0 in the absence of mass gap and infrared (IR) problem. For Mc → ∞, the initial UV divergent properties of QFT's are recovered and well-defined. In fact, the CES Mc and SES at μs = μc play the role of UV and IR cutoff energy scales respectively. It is strongly indicated that the conformal scaling symmetry and its breaking mechanism play an important role for understanding the mass gap and quark confinement. The new method is developed to be applicable for both underlying renormalizable QFT's and effective QFT's. It also leads to a set of conjectures on mathematically interesting numbers and functional limits which may provide deep insights in mathematics.

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Nisticò, Giuseppe. "Group Theoretical Derivation of Consistent Free Particle Theories." Foundations of Physics 50, no. 9 (August 14, 2020): 977–1007. http://dx.doi.org/10.1007/s10701-020-00364-2.

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AbstractThe difficulties of relativistic particle theories formulated by means of canonical quantization, such as those of Klein–Gordon and Dirac, ultimately led theoretical physicists to turn to quantum field theory to model elementary particle physics. In order to overcome these difficulties, the theories of the present approach are developed deductively from the physical principles that specify the system, without making use of canonical quantization. For a free particle these starting assumptions are invariance of the theory and covariance of position with respect to Poincaré transformations. In pursuing the approach, the effectiveness of group theoretical methods is exploited. The coherent development of our program has shown that robust classes of representations of the Poincaré group, discarded by the known particle theories, can in fact be taken as bases for perfectly consistent theories. For massive spin zero particles, six inequivalent theories have been determined, two of which do not correspond to any of the current ones; all of these theories overcome the difficulties of Klein–Gordon one. The present lack of the explicit transformation properties of position with respect to boosts prevents the complete determination of non zero spin particle theories. In the past a particular form of these transformation properties was adopted by Jordan and Mukunda. We check its consistency within the present approach and find that for spin $$\frac{1}{2}$$ 1 2 particles there is only one consistent theory, which is unitarily related to Dirac’s; yet, once again, it requires classes of irreducible representations previously discarded.

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Reichenberger, Andrea. "How to Teach History of Philosophy and Science: A Digital Based Case Study." Transversal: International Journal for the Historiography of Science, no. 5 (December 9, 2018): 84. http://dx.doi.org/10.24117/2526-2270.2018.i5.08.

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The following article describes a pilot study on the possible integration of digital historiography into teaching practice. It focuses on Émilie Du Châtelet’s considerations of space and time against the background of Leibniz’s program of analysis situs. Historians have characterized philosophical controversies on space and time as a dichotomy between the absolute and relational concepts of space and time. In response to this, the present case study pursues two aims: First, it shows that the common portrayal simplifies the complex pattern of change and the semantic shift from absolute-relational concepts of space and time to invariance and conservation principles. Second, against this background, I present the Online Reading Guide on Émilie Du Châtelet’s Foundations of Physics, a teaching and research project designed to help navigate Du Châtelet’s Institutions physiques (1740/42). This project makes Du Châtelet’s important text visible to a broad audience and allows for a more critical and deeper view on classical topics of the history of philosophy and science in a more accessible way than traditional introductions.

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Wang Jingxuan, 王竞煊, 汪毅 Wang Yi, 张佳琛 Zhang Jiachen, 蔡怀宇 Cai Huaiyu, and 陈晓冬 Chen Xiaodong. "一种基于射影不变原理的靶标及其解码方法." Laser & Optoelectronics Progress 58, no. 13 (2021): 1312001. http://dx.doi.org/10.3788/lop202158.1312001.

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Green, HS. "A Cyclic Symmetry Principle in Physics." Australian Journal of Physics 47, no. 1 (1994): 25. http://dx.doi.org/10.1071/ph940025.

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Many areas of modern physics are illuminated by the application of a symmetry principle, requiring the invariance of the relevant laws of physics under a group of transformations. This paper examines the implications and some of the applications of the principle of cyclic symmetry, especially in the areas of statistical mechanics and quantum mechanics, including quantized field theory. This principle requires invariance under the transformations of a finite group, which may be a Sylow 7r-group, a group of Lie type, or a symmetric group. The utility of the principle of cyclic invariance is demonstrated in finding solutions of the Yang-Baxter equation that include and generalize known solutions. It is shown that the Sylow 7r-groups have other uses, in providing a basis for a type of generalized quantum statistics, and in parametrising a new generalization of Lie groups, with associated algebras that include quantized algebras.

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Xu, Tianxu, Dong An, Yuetong Jia, and Yang Yue. "A Review: Point Cloud-Based 3D Human Joints Estimation." Sensors 21, no. 5 (March 1, 2021): 1684. http://dx.doi.org/10.3390/s21051684.

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Joint estimation of the human body is suitable for many fields such as human–computer interaction, autonomous driving, video analysis and virtual reality. Although many depth-based researches have been classified and generalized in previous review or survey papers, the point cloud-based pose estimation of human body is still difficult due to the disorder and rotation invariance of the point cloud. In this review, we summarize the recent development on the point cloud-based pose estimation of the human body. The existing works are divided into three categories based on their working principles, including template-based method, feature-based method and machine learning-based method. Especially, the significant works are highlighted with a detailed introduction to analyze their characteristics and limitations. The widely used datasets in the field are summarized, and quantitative comparisons are provided for the representative methods. Moreover, this review helps further understand the pertinent applications in many frontier research directions. Finally, we conclude the challenges involved and problems to be solved in future researches.

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Journal articles on the topic 'Invariance principles (Physics)'

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