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Journal articles on the topic 'Invariants and covariants'

Author: Grafiati

Published: 26 July 2024

Last updated: 31 July 2025

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1

Edge, W. L. "Geometry relevant to the binary quintic." Proceedings of the Edinburgh Mathematical Society 30, no. 2 (1987): 311–21. http://dx.doi.org/10.1017/s0013091500028376.

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The aim in this paper is to indicate one way of interpreting covariants of a binary quintic F geometrically, interpretations having been found recently [7] for its quadratic covariant 2C2, called Γ in [7], and its invariant I4. The symbol dCn will denote a covariant of order n in the binary variables x, y and degree d in the coefficients of F, Id being used in preference to dI0 for invariants. The sum d + n is 4 for both 2C2 and I4, and no other covariant affords as small a sum; so it is natural to have begun by interpreting these two and to use them as auxiliaries in interpreting others.

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2

Boularas, D., and Z. Bouzar. "Symplectic invariants and covariants of matrices." Linear and Multilinear Algebra 65, no. 8 (2016): 1503–28. http://dx.doi.org/10.1080/03081087.2016.1245273.

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3

KRUGLIKOV, BORIS, and VALENTIN LYCHAGIN. "INVARIANTS OF PSEUDOGROUP ACTIONS: HOMOLOGICAL METHODS AND FINITENESS THEOREM." International Journal of Geometric Methods in Modern Physics 03, no. 05n06 (2006): 1131–65. http://dx.doi.org/10.1142/s0219887806001478.

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We study the equivalence problem of submanifolds with respect to a transitive pseudogroup action. The corresponding differential invariants are determined via formal theory and lead to the notions of l-variants and l-covariants, even in the case of non-integrable pseudogroup. Their calculation is based on the cohomological machinery: we introduce a complex for covariants, define their cohomology and prove the finiteness theorem. This implies the well-known Lie–Tresse theorem about differential invariants. We also generalize this theorem to the case of pseudogroup action on differential equatio

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4

Ilash, N. B. "Hilbert polynomials of the algebras of $SL_ 2$-invariants." Carpathian Mathematical Publications 10, no. 2 (2018): 303–12. http://dx.doi.org/10.15330/cmp.10.2.303-312.

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We consider one of the fundamental problems of classical invariant theory, the research of Hilbert polynomials for an algebra of invariants of Lie group $SL_2$. Form of the Hilbert polynomials gives us important information about the structure of the algebra. Besides, the coefficients and the degree of the Hilbert polynomial play an important role in algebraic geometry. It is well known that the Hilbert function of the algebra $SL_n$-invariants is quasi-polynomial. The Cayley-Sylvester formula for calculation of values of the Hilbert function for algebra of covariants of binary $d$-form $\math

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Ilash, N. B. "Poincare series for the algebras of joint invariants and covariants of $n$ quadratic forms." Carpathian Mathematical Publications 9, no. 1 (2017): 57–62. http://dx.doi.org/10.15330/cmp.9.1.57-62.

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We consider one of the fundamental problems of classical invariant theory - the research of Poincare series for an algebra of invariants of Lie group $SL_2$. The first two terms of the Laurent series expansion of Poincare series at the point $z = 1$ give us important information about the structure of the algebra $\mathcal{I}_{d}.$ It was derived by Hilbert for the algebra ${\mathcal{I}_{d}=\mathbb{C}[V_d]^{\,SL_2}}$ of invariants for binary $d-$form (by $V_d$ denote the vector space over $\mathbb{C}$ consisting of all binary forms homogeneous of degree $d$). Springer got this result, using ex

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6

Ichinose, Shoichi. "Graphical representation of invariants and covariants in general relativity." Classical and Quantum Gravity 12, no. 4 (1995): 1021–54. http://dx.doi.org/10.1088/0264-9381/12/4/011.

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7

Ryb, Itai, and Roi Baer. "Combinatorial invariants and covariants as tools for conical intersections." Journal of Chemical Physics 121, no. 21 (2004): 10370–75. http://dx.doi.org/10.1063/1.1808695.

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8

Dhont, Guillaume, and Boris I. Zhilinskií. "The action of the orthogonal group on planar vectors: invariants, covariants and syzygies." Journal of Physics A: Mathematical and Theoretical 46, no. 45 (2013): 455202. http://dx.doi.org/10.1088/1751-8113/46/45/455202.

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9

Bedratyuk, Leonid. "The Poincaré series of the algebras of simultaneous invariants and covariants of two binary forms." Linear and Multilinear Algebra 58, no. 6 (2010): 789–803. http://dx.doi.org/10.1080/03081080903127262.

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10

Smirnov, Roman G., and Jin Yue. "Covariants, joint invariants and the problem of equivalence in the invariant theory of Killing tensors defined in pseudo-Riemannian spaces of constant curvature." Journal of Mathematical Physics 45, no. 11 (2004): 4141–63. http://dx.doi.org/10.1063/1.1805728.

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11

Mesquita, Afrânio Rubens de, Carlos Augusto De Sampaio França, and Marco Antonio Corrêa. "SEA LEVEL ANALYSES OF PSMSL SERIES BY PROXIMITY AND COLLINEARITY COEFFICIENTS." Revista Brasileira de Geofísica 31, no. 5 (2013): 23. http://dx.doi.org/10.22564/rbgf.v31i5.386.

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ABSTRACT. Annual mean sea level data distributed by PSMSL (Permanent Service for the Mean Sea Level) of IAPSO (International Association for the Physical Sciences of the Oceans) were analysed in the search for global sea level co-variants and invariants. The correlation coefﬁcient ρ , taken as a measure of collinearity ρc in time series, was shown to depend on the ratio of two variances and then invariant with the inclination β of the regression line yri(ti) = tan(β)xi + α , α the intercept, relative to the Cartesian coordinated axes. Also invariant with the trends βt is the distance i of the

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12

VAN TONDER, ANDRÉ. "WORLDSHEET COVARIANT PATH INTEGRAL QUANTIZATION OF STRINGS." International Journal of Modern Physics A 21, no. 32 (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 wide

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13

McNUTT, DAVID. "SPACETIMES WITH ALL SCALAR CURVATURE INVARIANTS IN TERMS OF A COSMOLOGICAL CONSTANT." International Journal of Modern Physics D 22, no. 02 (2013): 1350003. http://dx.doi.org/10.1142/s021827181350003x.

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In this paper we provide an invariant characterization for all spacetimes with all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives vanishing except those zeroth-order curvature invariants expressed as polynomials in Λ, the cosmological constant. Using this invariant description we provide an explicit forms for the metric.

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14

He, Yue, Xinwei Shen, Renzhe Xu, et al. "Covariate-Shift Generalization via Random Sample Weighting." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 10 (2023): 11828–36. http://dx.doi.org/10.1609/aaai.v37i10.26396.

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Shifts in the marginal distribution of covariates from training to the test phase, named covariate-shifts, often lead to unstable prediction performance across agnostic testing data, especially under model misspecification. Recent literature on invariant learning attempts to learn an invariant predictor from heterogeneous environments. However, the performance of the learned predictor depends heavily on the availability and quality of provided environments. In this paper, we propose a simple and effective non-parametric method for generating heterogeneous environments via Random Sample Weighti

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15

Khokhlov, S. V., and L. A. Ignatochkina. "Invariance of some classes of almost Hermitian structures concerning to the one-parameter group of diffeomorphisms generated by the Lie vector field." Differential Geometry of Manifolds of Figures, no. 53 (2022): 127–34. http://dx.doi.org/10.5922/0321-4796-2022-53-12.

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Finding the conditions for the invariance of geometric objects under the action of transformation groups is one of the main objects of geometric research. Almost Hermitian structures and structures of the Gray — Hervella classification on smooth manifolds are considered in this paper. All arguments are given using invariant Koszul’s calculus. Conditions for the invariance of the Kähler form in type structures are investigated and it is shown that the Kähler form is covariantly constant with respect to the Lie vector field. Conditions for the invariance of the Riemannian metric under the acti

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Pyun, Do Young, Heetae Cho, and Ho Keat Leng. "Applicability of belief measures for advertising to sponsorship in sport." International Journal of Sports Marketing and Sponsorship 21, no. 2 (2020): 351–69. http://dx.doi.org/10.1108/ijsms-06-2019-0059.

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PurposeWhile advertising and sponsorship are conceptually different, many studies have used the same measures for both constructs. The assumption is that respondents perceive both domains similarly. The purpose of this study was to test the invariance of the belief measures between the advertising and sponsorship measurement models across different consumer segments and to provide empirical justification for the practice.Design/methodology/approachTwo independent samples were recruited from two different consumer segments: university student consumers (n = 290) and general consumers (n = 324).

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17

GRÀCIA, XAVIER, and JAUME ROCA. "COVARIANT AND NONCOVARIANT GAUGE TRANSFORMATIONS FOR THE CONFORMAL PARTICLE." Modern Physics Letters A 08, no. 19 (1993): 1747–61. http://dx.doi.org/10.1142/s0217732393001483.

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A gauge-invariant conformal particle model is studied. Its Lagrangian gauge transformations are obtained in a covariant way using a kind of canonical generator. On the other hand, the Hamiltonian transformations cannot be written in a covariant form despite the covariance of the Hamiltonian constraints.

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18

MEYER, FRANK, and HAROLD STEINACKER. "GAUGE FIELD THEORY ON THE Eq(2)-COVARIANT PLANE." International Journal of Modern Physics A 19, no. 20 (2004): 3349–75. http://dx.doi.org/10.1142/s0217751x04019512.

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Gauge theory on the q-deformed two-dimensional Euclidean plane [Formula: see text] is studied using two different approaches. We first formulate the theory using the natural algebraic structures on [Formula: see text], such as a covariant differential calculus, a frame of one-forms and invariant integration. We then consider a suitable star product, and introduce a natural way to implement the Seiberg–Witten map. In both approaches, gauge invariance requires a suitable "measure" in the action, breaking the Eq(2)-invariance. Some possibilities to avoid this conclusion using additional terms in

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19

Rojas-Quintero, Juan Antonio, François Dubois, and Hedy César Ramírez-de-Ávila. "Riemannian Formulation of Pontryagin’s Maximum Principle for the Optimal Control of Robotic Manipulators." Mathematics 10, no. 7 (2022): 1117. http://dx.doi.org/10.3390/math10071117.

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In this work, we consider robotic systems for which the mass tensor is identified to be the metric in a Riemannian manifold. Cost functional invariance is achieved by constructing it with the identified metric. Optimal control evolution is revealed in the form of a covariant second-order ordinary differential equation featuring the Riemann curvature tensor that constrains the control variable. In Pontryagin’s framework of the maximum principle, the cost functional has a direct impact on the system Hamiltonian. It is regarded as the performance index, and optimal control variables are affected

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20

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 on

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21

Zhang, Yunsheng, Zijing Ren, Zichen Ding, Hong Qian, Haiqiang Li, and Chao Tao. "Co-ECL: Covariant Network with Equivariant Contrastive Learning for Oriented Object Detection in Remote Sensing Images." Remote Sensing 16, no. 3 (2024): 516. http://dx.doi.org/10.3390/rs16030516.

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Contrastive learning allows us to learn general features for downstream tasks without the need for labeled data by leveraging intrinsic signals within remote sensing images. Existing contrastive learning methods encourage invariant feature learning by bringing positive samples defined by random transformations in feature spaces closer, where transformed samples of the same image at different intensities are considered equivalent. However, remote sensing images differ from natural images in their top-down perspective results in the arbitrary orientation of objects and in that the images contain

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GRIGORE, D. R. "ON MANIFEST COVARIANCE CONDITION IN THE LAGRANGIAN FORMALISM." International Journal of Modern Physics A 07, no. 17 (1992): 4073–89. http://dx.doi.org/10.1142/s0217751x92001824.

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The manifest covariance condition for a Poincaré covariant theory is analyzed in the framework of the Lagrangian formalism in a systematic way. We prove that this result is of a kinematic nature and also show that in some cases one needs an appropriate generalization of the Lagrangian formalism. Then the manifest covariance condition is analyzed in a Galilei invariant theory, obtaining the most general type of interaction allowed by this condition.

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23

Jin, Shuai, and Frederick J. Boehmke. "Proper Specification of Nonproportional Hazards Corrections in Duration Models." Political Analysis 25, no. 1 (2017): 138–44. http://dx.doi.org/10.1017/pan.2016.16.

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Parametric and nonparametric duration models assume proportional hazards: The effect of a covariate on the hazard rate stays constant over time. Researchers have developed techniques to test and correct nonproportional hazards, including interacting the covariates with some function of time. Including this interaction term means that the specification now involves time-varying covariates, and the model specification should reflect this feature. However, in situations with no time-varying covariates initially, researchers often continue to model the duration with only time-invariant covariates.

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24

Toro, Ronald, Juan García-García, and Flor Zaldívar-Basurto. "Factorial analysis and invariance by sex and age of the Anger Rumination Scale ARS Spanish version." Anales de Psicología 36, no. 3 (2020): 475–82. http://dx.doi.org/10.6018/analesps.394021.

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La rumiación ira es pensamiento perseverativo sobre un evento personalmente significativo ocurrido a la persona o las demás que conlleva a la ira y se constituye como factor de riesgo para la agresión. El objetivo fue realizar un análisis factorial confirmatorio e invarianza por sexo y edades de la Anger Rumination Scale [ARS]. Se conformó una muestra no probabilística de 640 personas con entre 18 y 63 años (M = 31.07, SD = 11.27), agrupadas por sexos (252 hombres, 378 mujeres) y edades (278 menores de 25 años, 352 mayores de 25 años). Los instrumentos fueron el ARS y el cuestionario de agresi

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25

Carter, B., and B. Gaffet. "Standard covariant formulation for perfect-fluid dynamics." Journal of Fluid Mechanics 186 (January 1988): 1–24. http://dx.doi.org/10.1017/s0022112088000011.

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After a brief description of the Milne generalization of the Galilean invariance group for the space–time of Newtonian kinematics, it is shown how the generalized Eulerian dynamical equations for the motion of a multiconstituent perfect (nonconducting) fluid can be expressed in terms of interior products of current 4-vectors with exterior derivatives of the appropriate 4-momentum 1-forms (whose role is central in this approach) in a fully covariant standard form whose structure is identical in the Newtonian case to that of the corresponding equation for the case of (special or general) relativ

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Piacitelli, Gherardo. "Twisted Covariance as a Non-Invariant Restriction of the Fully Covariant DFR Model." Communications in Mathematical Physics 295, no. 3 (2010): 701–29. http://dx.doi.org/10.1007/s00220-010-0988-9.

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27

GUENDELMAN, E. I. "SCALE INVARIANCE AND VACUUM ENERGY." Modern Physics Letters A 14, no. 21 (1999): 1397–401. http://dx.doi.org/10.1142/s0217732399001498.

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The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. Scale invariance is considered in the context of a gravitational theory where the action, in the first-order formalism, is of the form [Formula: see text] where Φ is a density built out of degrees of freedom independent of the metric. For global scale invariance, a "dilaton" ϕ has to be introduced, with nontrivial potentials V(ϕ)=f1eαϕ in L1 and U(ϕ)=f2e2αϕ in L2. This leads to nontrivial mass generation and a potential for ϕ which is interesting for new inflation. Scale invariant mass terms

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28

Zhang, Peng, Wen Juan Qi, and Zi Li Deng. "Covariance Intersection Fusion Kalman Estimator for Multi-Sensor System with Measurements Delays." Applied Mechanics and Materials 475-476 (December 2013): 460–65. http://dx.doi.org/10.4028/www.scientific.net/amm.475-476.460.

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To handle the state estimation fusion problem between local estimation errors for the system with unknown cross-covariances and to avoid a large computation complexity of cross-covariances, for a multi-sensor linear discrete time-invariant stochastic system with time-delayed measurements, by the measurement transformation method, an equivalent system without measurement delays is obtained, and then using the covariance intersection (CI) fusion method, the covariance intersection fusion steady-state Kalman estimator is presented. It is proved that its accuracy is higher than that of each local

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29

ARNONE, STEFANO, YURI A. KUBYSHIN, TIM R. MORRIS, and JOHN F. TIGHE. "GAUGE-INVARIANT REGULARISATION VIA SU(N|N)." International Journal of Modern Physics A 17, no. 17 (2002): 2283–329. http://dx.doi.org/10.1142/s0217751x02009722.

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We construct a gauge-invariant regularisation scheme for pure SU(N) Yang–Mills theory in dimension four or less (for N = ∞ in all dimensions), with a physical cutoff scale Λ, by using covariant higher derivatives and spontaneously broken SU(N|N) supergauge invariance. Providing their powers are within certain ranges, the covariant higher derivatives cure the superficial divergence of all but a set of one-loop graphs. The finiteness of these latter graphs is ensured by properties of the supergroup and gauge invariance. In the limit Λ → ∞, all the regulator fields decouple and unitarity is recov

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30

Hammond, Richard T. "Electromagnetic spin creates torsion." International Journal of Modern Physics D 27, no. 14 (2018): 1847005. http://dx.doi.org/10.1142/s0218271818470053.

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It is shown the intrinsic spin, and only the spin, of the electromagnetic field creates torsion. The struggle raged for decades: How to reconcile the facts that photons have spin, but minimal coupling breaks gauge invariance and therefore must be abandoned, leaving us with the unphysical situation in which spin does not create torsion. By generalizing the gauge freedom of the torsion field, a covariant, gauge-invariant description is found whereby the electromagnetic spin creates a torsion field. In fact, it is shown if electromagnetic gauge invariance holds, torsion must be present.

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Fernández, Antonio, Pedro L. Garcı́a, and J. Muñoz Masqué. "Gauge-invariant covariant Hamiltonians." Journal of Mathematical Physics 41, no. 8 (2000): 5292–303. http://dx.doi.org/10.1063/1.533410.

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CAPRI, A. Z., and S. M. ROY. "LORENTZ-COVARIANT AND GAUGE-INVARIANT INSTANTANEOUS VACUUM FOR EXTERNAL FIELD PROBLEMS." International Journal of Modern Physics A 09, no. 07 (1994): 1025–41. http://dx.doi.org/10.1142/s0217751x94000479.

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For a Dirac field coupled to time-dependent external electromagnetic field we define an instantaneous (on a fixed spacelike surface) causal vacuum respecting Lorentz covariance and gauge invariance. The instantaneous particle states on this surface are then defined covariantly and connected to states at another time by a Bogoliubov transformation.

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JORGENSEN, PALLE E. T., and XIU-CHI QUAN. "COVARIANCE GROUP C*-ALGEBRAS AND GALOIS CORRESPONDENCE." International Journal of Mathematics 02, no. 06 (1991): 673–99. http://dx.doi.org/10.1142/s0129167x91000375.

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The main purpose of this paper is to establish a Galois correspondence for a given covariant group system, its associated C*-algebra and Hopf C*-algebra. On the way to this, we first study covariance group C*-algebras and their representations, and prove a result which is simpler but yet very similar to the C*-algebra case in the main body of the paper. We then show that there is a Galois correspondence between the lattice of normal subgroups of the given covariant group system and a corresponding lattice of certain invariant *-subalgebras of the covariant group C*-algebra; in particular, ther

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MELROSE, D. B. "Covariant form of Trubnikov's response tensor for a relativistic magnetized thermal plasma." Journal of Plasma Physics 57, no. 2 (1997): 479–88. http://dx.doi.org/10.1017/s0022377896004989.

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A covariant version of Vlasov theory is used to derive the linear response 4-tensor for a relativistic magnetized thermal plasma, generalizing Trubnikov's 3-tensor form. The charge-continuity and gauge-invariance conditions imply a set of integral identities, and use of these identities allows one to derive a manifestly gauge invariant form for the response 4-tensor. This form implies an alternative version of Trubnikov's 3-tensor. The different versions lead to different expressions in the weakly relativistic small-gyroradius limit. Arguments are given as to how this inconsistency should be r

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GUENDELMAN, E. I. "SCALE SYMMETRY BREAKING FROM THE DYNAMICS OF MAXIMAL RANK GAUGE FIELD STRENGTHS." International Journal of Modern Physics A 19, no. 19 (2004): 3255–64. http://dx.doi.org/10.1142/s0217751x04019317.

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Scale invariant theories which contain maximal rank gauge field strengths (of D indices in D dimensions) are studied. The integration of the equations of motion of these gauge fields leads to the scale symmetry breaking of scale invariance. The cases in study are (i) the spontaneous generation of r-1 potentials in particle mechanics in a theory that contains only r-2 potentials in the scale invariant phase, (ii) mass generation in scalar field theories, (iii) generation of nontrivial dilaton potentials in generally covariant theories, and (iv) spontaneous generation of confining behavior in ga

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ITIN, Y. "CONSERVED CURRENT FOR GENERAL TELEPARALLEL MODELS." International Journal of Modern Physics A 17, no. 20 (2002): 2765. http://dx.doi.org/10.1142/s0217751x02011928.

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The obstruction for the existence of an energy-momentum tensor for the gravitational field in GR is connected with vanishing of first order invariants in (pseudo) Riemannian geometry. This specific geometric property is not valid in alternative geometrical structures1,2. A parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields ϑa is considered. A general 3-parameter class of global Lorentz invariant teleparallel models is considered. It includes a 1-parameter subclass of models with the Schwarzschild coframe solution (generalized teleparallel equivalent of grav

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Colléaux, Aimeric, Stefano Chinaglia, and Sergio Zerbini. "Nonpolynomial Lagrangian approach to regular black holes." International Journal of Modern Physics D 27, no. 03 (2018): 1830002. http://dx.doi.org/10.1142/s0218271818300021.

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We present a review on Lagrangian models admitting spherically symmetric regular black holes (RBHs), and cosmological bounce solutions. Nonlinear electrodynamics, nonpolynomial gravity, and fluid approaches are explained in details. They consist respectively in a gauge invariant generalization of the Maxwell–Lagrangian, in modifications of the Einstein–Hilbert action via nonpolynomial curvature invariants, and finally in the reconstruction of density profiles able to cure the central singularity of black holes. The nonpolynomial gravity curvature invariants have the special property to be seco

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BENTALHA, Z., and M. TAHIRI. "A NOTE ON SLq(2) COVARIANCE AND QUANTUM EUCLIDEAN PLANE." Modern Physics Letters A 22, no. 14 (2007): 1031–37. http://dx.doi.org/10.1142/s0217732307021342.

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A quantum analogue of SL(2) covariance is given. The method consists of defining a bilinear form on SL q(2) co-module, then we ask the defined form to be invariant under SL q(2) co-actions. We showed that the required invariance leads to the standard algebraic structure of SL q(2) ideal. On the other hand, the geometry of the three-dimensional quantum Euclidean space has been evoked by computing the quantum Euclidean metric, the quantum Euclidean "distance" (the central element) and the relation of orthogonality of SO q(3) quantum group.

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SATHIAPALAN, B. "LOOP VARIABLES AND THE INTERACTING OPEN STRING IN A CURVED BACKGROUND." Modern Physics Letters A 20, no. 14 (2005): 1037–45. http://dx.doi.org/10.1142/s0217732305017305.

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Applying the loop variable proposal to a sigma model (with boundary) in a curved target space, we give a systematic method for writing the gauge and generally covariant interacting equations of motion for the modes of the open string in a curved background. As in the free case described in an earlier paper, the equations are obtained by covariantizing the flat space (gauge invariant) interacting equations and then demanding gauge invariance in the curved background. The resulting equation has the form of a sum of terms that would individually be gauge invariant in flat space or at zero interac

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HATZINIKITAS, AGAPITOS, and IOANNIS SMYRNAKIS. "CLOSED BOSONIC STRING PARTITION FUNCTION IN TIME INDEPENDENT EXACT pp-WAVE BACKGROUND." International Journal of Modern Physics A 21, no. 05 (2006): 995–1013. http://dx.doi.org/10.1142/s0217751x06025493.

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The modular invariance of the one-loop partition function of the closed bosonic string in four dimensions in the presence of certain homogeneous exact pp -wave backgrounds is studied. In the absence of an axion field, the partition function is found to be modular invariant and equal to the free field partition function. The partition function remains unchanged also in the presence of a fixed axion field. However, in this case, the covariant form of the action suggests summation over all possible twists generated by the axion field. This is shown to modify the partition function. In the light-c

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SATHIAPALAN, B. "PROPER TIME FORMALISM AND GAUGE INVARIANCE IN OPEN STRING INTERACTIONS." Modern Physics Letters A 09, no. 18 (1994): 1681–93. http://dx.doi.org/10.1142/s0217732394001520.

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The issue of gauge invariances in the sigma model formalism is discussed at the free and interacting level. The problem of deriving gauge invariant interacting equations can be addressed using the proper time formalism. This formalism is discussed, both for point particles and strings. The covariant Klein-Gordon equation arises in a geometric way from the boundary terms. This formalism is similar to the background independent open string formalism introduced by Witten.

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Zhang, Liyi, Zengguang Tian, Yi Tang, and Zuo Jiang. "Task-Covariant Representations for Few-Shot Learning on Remote Sensing Images." Mathematics 11, no. 8 (2023): 1930. http://dx.doi.org/10.3390/math11081930.

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In the regression and classification of remotely sensed images through meta-learning, techniques exploit task-invariant information to quickly adapt to new tasks with fewer gradient updates. Despite its usefulness, task-invariant information alone may not effectively capture task-specific knowledge, leading to reduced model performance on new tasks. As a result, the concept of task-covariance has gained significant attention from researchers. We propose task-covariant representations for few-shot Learning on remote sensing images that utilizes capsule networks to effectively represent the cova

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Papini, Giorgio. "Covariance and gauge invariance in relativistic theories of gravity." Modern Physics Letters A 29, no. 14 (2014): 1450075. http://dx.doi.org/10.1142/s0217732314500758.

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Any metric theory of gravity whose interaction with quantum particles is described by a covariant wave equation is equivalent to a vector theory that satisfies Maxwell-type equations identically. This result does not depend on any particular set of field equations for the metric tensor, but only on covariance. It is derived in the linear case, but can be extended to any order of approximation in the metric deviation. In this formulation of the interaction of gravity with matter, angular momentum and momentum are conserved locally.

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BARUT, A. O., and M. PAVŠIČ. "A COVARIANT CANONICAL DECOMPOSITION OF THE BOSONIC AND SPINNING EXTENDED OBJECTS WITH ELECTRIC CHARGE." Modern Physics Letters A 07, no. 15 (1992): 1381–89. http://dx.doi.org/10.1142/s0217732392001051.

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By introducing a time-like vector field na (hence a choice of an invariant time parameter τ) the action of a spinning extended object in d dimensions can be covariantly decomposed into the analog of a center of mass part and a space-like internal part. In this way the action has the same form as that of a point particle which is covenient for the interpretation of the theory, its covariant canonical quantization and for the definition of the form factors.

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McKeon, D. G. C. "One-loop effects in N = 4 supersymmetry." Canadian Journal of Physics 74, no. 3-4 (1996): 176–81. http://dx.doi.org/10.1139/p96-028.

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It has been demonstrated that in massless supersymmetric theories, finite radiative corrections to the superpotential can occur (viz. the nonrenormalization theorems can be circumvented). In this paper, we examine the consequences of this in N = 4 supersymmetric Yang–Mills theory, a model in which the β function is known to be zero. It is shown that radiative corrections to the superpotential arise at one loop order in this theory contrary to the expectations of the nonrenormalization theorem, but that their form depends on which formulation of the model is used. When one uses a superfield for

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ANEZIRIS, C., A. P. BALACHANDRAN, M. BOURDEAU, S. JO, R. D. SORKIN, and T. R. RAMADAS. "ASPECTS OF SPIN AND STATISTICS IN GENERALLY COVARIANT THEORIES." International Journal of Modern Physics A 04, no. 20 (1989): 5459–510. http://dx.doi.org/10.1142/s0217751x8900234x.

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In this paper, we explore the consequences of diffeomorphism invariance in generally covariant theories. Such theories in two and three dimensions are known to admit topological excitations called geons. It is shown by specific examples that a quantum state of two identical geons may not be an eigenstate of the geon exchange operator, which means that a geon may have no definite statistics. As shown before by Sorkin and as discussed further here, it may also happen, for instance, that in 3 + 1 dimensions a tensorial (spinorial) geon obeys Fermi (Bose) statistics, while in 2 + 1 dimensions an "

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Broer, Abraham, and Jianjun Chuai. "Modules of covariants in modular invariant theory." Proceedings of the London Mathematical Society 100, no. 3 (2009): 705–35. http://dx.doi.org/10.1112/plms/pdp044.

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BECAR, RAMÓN, and P. A. GONZÁLEZ. "HAWKING RADIATION FOR SCALAR AND DIRAC FIELDS IN FIVE-DIMENSIONAL DILATONIC BLACK HOLE VIA ANOMALIES." International Journal of Modern Physics D 21, no. 03 (2012): 1250030. http://dx.doi.org/10.1142/s0218271812500307.

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We study massive scalar fields and Dirac fields propagating in a five-dimensional dilatonic black hole background. We expose that for both fields the physics can be described by a two-dimensional theory, near the horizon. Then, in this limit, by applying the covariant anomalies method we find the Hawking flux by restoring the gauge invariance and the general coordinate covariance, which coincides with the flux obtained from integrating the Planck distribution for fermions.

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de Haro, Jaume. "On the Hole Argument and the Physical Interpretation of General Relativity." Universe 10, no. 2 (2024): 91. http://dx.doi.org/10.3390/universe10020091.

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Einstein presented the Hole Argument against General Covariance, understood as invariance with respect to a change in coordinates, as a consequence of his initial failure to obtain covariant equations that, in the weak static limit, contain Newton’s law. Fortunately, about two years later, Einstein returned to General Covariance, and found these famous equations of gravity. However, the rejection of his Hole Argument carries a totally different vision of space-time. Its substantivalism notion, which is an essential ingredient in Newtonian theory and also in his special theory of relativity, ha

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Stoica, O. C. "On singular semi-Riemannian manifolds." International Journal of Geometric Methods in Modern Physics 11, no. 05 (2014): 1450041. http://dx.doi.org/10.1142/s0219887814500418.

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On a Riemannian or a semi-Riemannian manifold, the metric determines invariants like the Levi-Civita connection and the Riemann curvature. If the metric becomes degenerate (as in singular semi-Riemannian geometry), these constructions no longer work, because they are based on the inverse of the metric, and on related operations like the contraction between covariant indices. In this paper, we develop the geometry of singular semi-Riemannian manifolds. First, we introduce an invariant and canonical contraction between covariant indices, applicable even for degenerate metrics. This contraction a

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