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Journal articles on the topic 'Manifolds with constant energy'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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1

Perrone, D., and L. Vergori. "Stability of contact metric manifolds and unit vector fields of minimum energy." Bulletin of the Australian Mathematical Society 76, no. 2 (2007): 269–83. http://dx.doi.org/10.1017/s0004972700039654.

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In this paper we obtain criteria of stability for ηEinstein k-contact manifolds, for Sasakian manifolds of constant ϕ-sectional curvature and for 3-dimensional Sasakian manifolds. Moreover, we show that a stable compact Einstein contact metric manifold M is Sasakian if and only if the Reeb vector field ξ minimises the energy functional. In particular, the Reeb vector field of a Sasakian manifold M of constant ϕ-holomorphic sectional curvature +1 minimises the energy functional if and only if M is not simply connected.

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2

Winterbone, D. E., J. R. Nichols, and G. I. Alexander. "Efficiency of the Manifolds of Turbocharged Engines." Proceedings of the Institution of Mechanical Engineers, Part D: Transport Engineering 199, no. 2 (1985): 137–50. http://dx.doi.org/10.1243/pime_proc_1985_199_150_01.

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For many years there has been debate about the most efficient way of turbocharging diesel engines, particularly medium and slow speed ones. There are advocates of pulse charging, pulse converting and constant pressure exhaust systems; these techniques counterbalance the variations of transmission efficiency with turbine efficiency. A major difficulty in assessing the methods has been locating the regions of energy loss in the manifold. This paper describes a wave action method of evaluating the transmission of energy from the cylinder through the exhaust valve, via the pipes and junctions to t

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3

EFREMOV, VLADIMIR N., ALFONSO M. HERNÁNDEZ MAGDALENO, and CLAUDIA MORENO. "TOPOLOGICAL ORIGIN OF THE COUPLING CONSTANTS HIERARCHY IN KALUZA–KLEIN APPROACH." International Journal of Modern Physics A 25, no. 13 (2010): 2699–733. http://dx.doi.org/10.1142/s0217751x10048482.

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We consider an Abelian BF-model in the frame of ten-dimensional Kaluza–Klein approach on the space T2×X×M, where X belongs to the class of four-dimension decorated plumbed cobordisms (dp-cobordisms) and M is an An-1-singularity resolution manifold homeomorphic to a compactified ALE space. These four-dimensional manifolds with boundaries possess nontrivial cohomology properties that lead to a specific generalization of the Dirac quantization conditions and enables us to express classical partition functions in terms of 4-form fluxes through the direct product of nontrivial 2-cycles associated w

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4

Chen, Qun. "Stability and constant boundary-value problems of harmonic maps with potential." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 68, no. 2 (2000): 145–54. http://dx.doi.org/10.1017/s1446788700001907.

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AbstractLet M, N be Riemannian manifolds, f: M → N a harmonic map with potential H, namely, a smooth critical point of the functional EH(f) = ∫M[e(f)−H(f)], where e(f) is the energy density of f. Some results concerning the stability of these maps between spheres and any Riemannian manifold are given. For a general class of M, this paper also gives a result on the constant boundary-value problem which generalizes the result of Karcher-Wood even in the case of the usual harmonic maps. It can also be applied to the static Landau-Lifshitz equations.

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Shaikh, Absos Ali, Biswa Ranjan Datta, Akram Ali, and Ali H. Alkhaldi. "LCS-manifolds and Ricci solitons." International Journal of Geometric Methods in Modern Physics 18, no. 09 (2021): 2150138. http://dx.doi.org/10.1142/s0219887821501383.

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This paper is concerned with the study of [Formula: see text]-manifolds and Ricci solitons. It is shown that in a [Formula: see text]-spacetime, the fluid has vanishing vorticity and vanishing shear. It is found that in an [Formula: see text]-manifold, [Formula: see text] is an irrotational vector field, where [Formula: see text] is a non-zero smooth scalar function. It is proved that in a [Formula: see text]-spacetime with generator vector field [Formula: see text] obeying Einstein equation, [Formula: see text] or [Formula: see text] according to [Formula: see text] or [Formula: see text], wh

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6

OH, JOHN J., and HYUN SEOK YANG. "EINSTEIN MANIFOLDS AS YANG–MILLS INSTANTONS." Modern Physics Letters A 28, no. 21 (2013): 1350097. http://dx.doi.org/10.1142/s0217732313500971.

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It is well known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equation from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang–Mills gauge theory and so Einstein manifolds correspond to Yang–Mills instantons in SO (4) = S

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Gutiérrez-Piñeres, Antonio C., Cesar S. López-Monsalvo, and Francisco Nettel. "Two-Dimensional Einstein Manifolds in Geometrothermodynamics." Advances in High Energy Physics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/967618.

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We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In particular, for systems constrained by the vanishing of the Hessian curvature we write down the systems of partial differential equations. In such a case it is possible to find a subset of solutions lying on a circumference in an abstract space constructed from the first derivatives of the isothermal coordinates. We conjecture that solutions on the characteristic

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8

Vishal, V., B. Siddharth, and C. Venkatachalam. "On the Mathematical Analysis of Black-Hole Information Loss Paradox." International Letters of Chemistry, Physics and Astronomy 18 (September 2013): 8–12. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.18.8.

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A Black-hole is an astronomical entity which possesses infinite density at its gravitational singularity or singular point. The capacity of a black-hole to completely rip-off an entire solar system without leaving any evidence is to be noted. A debate has been going on over the past few decades regarding the information storage in black-holes. The discovery of Hawking radiation, which predicts complete evaporation of mass violates unitarity ie. Conservation of probability and energy fails. Recent discoveries suggest that regular remnant of black-hole survives evaporation , as a result informat

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9

SARISAMAN, MUSTAFA. "PSEUDODUALITY IN SUPERSYMMETRIC SIGMA MODELS." International Journal of Modern Physics A 25, no. 15 (2010): 2997–3023. http://dx.doi.org/10.1142/s0217751x10048998.

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We study the pseudoduality transformation in supersymmetric sigma models. We generalize the classical construction of pseudoduality transformation to supersymmetric case. We perform this both by component expansion method on manifold [Formula: see text] and by orthonormal coframe method on manifold [Formula: see text]. The component expansion method yields the result that pseudoduality tranformation is not invertible at all points and occurs from all points on one manifold to only one point where Riemann normal coordinates are valid on the second manifold. Torsion of the sigma model on [Formul

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10

Santos, Almir Silva. "A Construction of Constant Scalar Curvature Manifolds with Delaunay-type Ends." Annales Henri Poincaré 10, no. 8 (2010): 1487–535. http://dx.doi.org/10.1007/s00023-010-0024-9.

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11

Sako, A. "Topological Symmetry Breaking on Einstein Manifolds." International Journal of Modern Physics A 12, no. 10 (1997): 1915–31. http://dx.doi.org/10.1142/s0217751x97001201.

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It is known that if gauge conditions have Gribov zero modes, then topological symmetry is broken. In this paper we apply it to the Witten type topological gravitational theory in dimension n ≥ 3. Our choice of the gauge condition for conformal invariance is R + α = 0, where R is the Ricci scalar curvature. We find when α ≠ 0, topological symmetry is not broken, but when α = 0 and solutions of the Einstein equations exist then topological symmetry is broken. These conditions connect to the Yamabe conjecture, namely negative constant scalar curvature exist on manifolds of any topology, but exist

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12

Naderi, F., A. Rezaei-Aghdam, and F. Darabi. "Gravity and induced matter on nearly Kähler manifolds." International Journal of Modern Physics A 30, no. 03 (2015): 1550015. http://dx.doi.org/10.1142/s0217751x15500153.

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We show that the conservation of energy–momentum tensor of a gravitational model with Einstein–Hilbert like action on a nearly Kähler manifold with the scalar curvature of a curvature-like tensor, is consistent with the nearly Kähler properties. In this way, the nearly Kähler structure is automatically manifested in the action as a induced matter field. As an example of nearly Kähler manifold, we consider the group manifold of R×II ×S3×S3 on which we identify a nearly Kähler structure and solve the Einstein equations to interpret the model. It is shown that the nearly Kähler structure in this

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13

Marongwe, Stuart. "On the Electromagnetic Vacuum Origins of Dark Energy, Dark Matter, and Astrophysical Jets." Advances in High Energy Physics 2021 (April 12, 2021): 1–8. http://dx.doi.org/10.1155/2021/5588662.

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We use a semiclassical version of the Nexus paradigm of quantum gravity in which the quantum vacuum at large scales is dominated by the second quantized electromagnetic field to demonstrate that a virtual photon field can affect the geometric evolution of Einstein manifolds or Ricci solitons. This phenomenon offers a cogent explanation of the origins of astrophysical jets, the cosmological constant, and a means of detecting galactic dark matter.

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14

Yun, Gabjin. "Spectral geometry of harmonic maps into warped product manifolds II." International Journal of Mathematics and Mathematical Sciences 27, no. 6 (2001): 327–39. http://dx.doi.org/10.1155/s0161171201007098.

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Let(Mn,g)be a closed Riemannian manifold andNa warped product manifold of two space forms. We investigate geometric properties by the spectra of the Jacobi operator of a harmonic mapϕ:M→N. In particular, we show ifNis a warped product manifold of Euclidean space with a space form andϕ,ψ:M→Nare two projectively harmonic maps, then the energy ofϕandψare equal up to constant ifϕandψare isospectral. Besides, we recover and improve some results by Kang, Ki, and Pak (1997) and Urakawa (1989).

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15

ISIDRO, JOSÉ M. "NON-ABELIAN POISSON MANIFOLDS FROM D-BRANES." Modern Physics Letters A 19, no. 34 (2004): 2541–48. http://dx.doi.org/10.1142/s0217732304015671.

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Superimposed D-branes have matrix-valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics where the multiplication law for coordinates and/or momenta, being given by matrix multiplication, is non-Abelian. Quantization further introduces noncommutativity as a deformation in powers of Planck's constant ℏ. Given an arbitrary simple Lie algebra [Formula: see text] and an arbitrary Poisson manifold ℳ, both finite-dimensional, we define a corresponding C⋆

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BUCHBINDER, I. L., V. A. KRYKHTIN, and P. M. LAVROV. "ON MANIFOLDS ADMITTING THE CONSISTENT LAGRANGIAN FORMULATION FOR HIGHER SPIN FIELDS." Modern Physics Letters A 26, no. 16 (2011): 1183–96. http://dx.doi.org/10.1142/s0217732311035535.

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We study a possibility of Lagrangian formulation for free massive higher spin bosonic totally symmetric tensor field on the background manifold characterizing by the arbitrary metric, vector and third-rank tensor fields in the framework of BRST approach. Assuming analytical dependence on the mass, curvatures and the other background fields in the Lagrangian and using the most general linearized ansatz for transversality condition, we prove that the consistent formulation is possible only in constant curvature space and that there is only a trivial possibility to include the vector and third-ra

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17

Wang, Youde. "Harmonic maps from noncompact Riemannian manifolds with non-negative Ricci curvature outside a compact set." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 124, no. 6 (1994): 1259–75. http://dx.doi.org/10.1017/s0308210500030249.

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In this paper we prove the uniqueness and existence of harmonic maps of finite energy from a complete, noncompact Riemannian manifold (M, g) with Sobolev constant S2(M) > 0 and Ricci curvature Ric (M) ≧ 0 outside some compact subset, into a complete manifold of nonpositive curvature or a regular ball. In particular, we prove the uniqueness and existence of bounded harmonic functions on (M, g).

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18

Agop, Maricel, Alina Gavriluţ, and Elena Rezuş. "Implications of Onicescu's informational energy in some fundamental physical models." International Journal of Modern Physics B 29, no. 07 (2015): 1550045. http://dx.doi.org/10.1142/s0217979215500459.

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Correlating Shannon's maximum informational entropy variational principle with the constant value of Onicescu's informational energy, the uncertainty relations for canonical systems with SL(2R) invariance are obtained. The constant value of Onicescu's informational energy corresponds, through transitivity manifolds of the SL(2R) group, to the ergodic theorem and, in particular case of a linear oscillator, to a quantification condition. Specifying de Broglie's idea by a periodic field in a complex coordinate, it is proved that the oscillator synchronization group of the same ensemble is still a

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19

Matveev, S. V., and A. T. Fomenko. "Constant energy surfaces of Hamiltonian systems, enumeration of three-dimensional manifolds in increasing order of complexity, and computation of volumes of closed hyperbolic manifolds." Russian Mathematical Surveys 43, no. 1 (1988): 3–24. http://dx.doi.org/10.1070/rm1988v043n01abeh001554.

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20

ARIK, M., and V. GABAY. "MASSLESS SCALAR FIELDS IN NON-ABELIAN KALUZA-KLEIN THEORY." International Journal of Modern Physics A 09, no. 04 (1994): 507–15. http://dx.doi.org/10.1142/s0217751x94000248.

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We investigate the presence of massless scalar fields in a Kaluza—Klein theory based on a dimensionally continued Euler-form action. We show that massless scalar fields exist provided that the internal space is a direct product of two irreducible manifolds. The condition of a vanishing effective four-dimensional cosmological constant and the presence of a graviton, gauge fields and massless scalar fields can be satisfied if both irreducible manifolds have odd dimensions and the sum of these dimensions is equal to the dimension of the Euler form.

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21

Bae, Youngjin, Kevin Wiegand, and Kai Zehmisch. "Periodic orbits in virtually contact structures." Journal of Topology and Analysis 12, no. 02 (2018): 371–418. http://dx.doi.org/10.1142/s1793525319500481.

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We prove that certain non-exact magnetic Hamiltonian systems on products of closed hyperbolic surfaces and with a potential function of large oscillation admit non-constant contractible periodic solutions of energy below the Mañé critical value. For that we develop a theory of holomorphic curves in symplectizations of non-compact contact manifolds that arise as the covering space of a virtually contact structure whose contact form is bounded with all derivatives up to order three.

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22

FERRARI, FRANCO. "FIELD THEORIES ON THE POINCARÉ DISK." International Journal of Modern Physics A 11, no. 30 (1996): 5389–404. http://dx.doi.org/10.1142/s0217751x96002467.

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The massive scalar field theory and the chiral Schwinger model are quantized on a Poincaré disk of radius ρ. The amplitudes are derived in terms of Legendre functions. The behavior at long distances and near the boundary of some of the relevant correlation functions is studied. The exact computation of the chiral determinant appearing in the Schwinger model is obtained exploiting perturbation theory. This calculation poses interesting mathematical problems, as the Poincaré disk is a noncompact manifold with a metric tensor which diverges when it approaches the boundary. The results presented i

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23

ABE, MITSUKO, AKIKA NAKAMICHI, and TATSUYA UENO. "MODULI SPACE OF TOPOLOGICAL TWO-FORM GRAVITY." Modern Physics Letters A 09, no. 10 (1994): 895–901. http://dx.doi.org/10.1142/s021773239400071x.

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We propose a topological version of four-dimensional (Euclidean) Einstein gravity, in which anti-self-dual two-forms and an SU(2) connection are used as fundamental fields. The theory describes the moduli space of conformally self-dual Einstein manifolds. In the presence of a cosmological constant, we evaluate the index of the elliptic complex associated with the moduli space.

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24

GURUSWAMY, S., and P. VITALE. "CORRELATION FUNCTIONS OF A CONFORMAL FIELD THEORY IN THREE DIMENSIONS." Modern Physics Letters A 11, no. 13 (1996): 1047–59. http://dx.doi.org/10.1142/s0217732396001089.

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We derive explicit forms of the two-point correlation functions of the O(N) nonlinear sigma model at the critical point, in the large-N limit, on various three-dimensional manifolds of constant curvature. The two-point correlation function, G(x, y), is the only n-point correlation function which survives in this limit. We analyze the short distance and long distance behaviors of G(x, y). It is shown that G(x, y) decays exponentially with the Riemannian distance on the spaces R2×S1, S1×S1×R, S2×R, H2×R. The decay on R3 is of course a power law. We show that the scale for the correlation length

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VOLOVICH, I. V. "AFFINE STRINGS." Modern Physics Letters A 08, no. 19 (1993): 1827–34. http://dx.doi.org/10.1142/s0217732393001550.

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A new model of bosonic strings is considered. An action of the model is the sum of the standard string action and a term describing an interaction of a metric with a linear (affine) connection. The Lagrangian of this interaction is an arbitrary analytic function f(R) of the scalar curvature. This is a classically integrable model. The space of classical solutions of the theory consists of sectors with constant curvature. In each sector the equations of motion reduce to the standard string equations and to an additional constant curvature equation for the linear connection. A bifurcation in the

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Gover, A. Rod, and Andrew Waldron. "Renormalized volumes with boundary." Communications in Contemporary Mathematics 21, no. 02 (2019): 1850030. http://dx.doi.org/10.1142/s021919971850030x.

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We develop a general regulated volume expansion for the volume of a manifold with boundary whose measure is suitably singular along a separating hypersurface. The expansion is shown to have a regulator independent anomaly term and a renormalized volume term given by the primitive of an associated anomaly operator. These results apply to a wide range of structures. We detail applications in the setting of measures derived from a conformally singular metric. In particular, we show that the anomaly generates invariant ([Formula: see text]-curvature, transgression)-type pairs for hypersurfaces wit

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27

Sjöström Dyrefelt, Zakarias. "On K-Polystability of cscK Manifolds with Transcendental Cohomology Class." International Mathematics Research Notices 2020, no. 9 (2018): 2769–817. http://dx.doi.org/10.1093/imrn/rny094.

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Abstract In this paper we study K-polystability of arbitrary (possibly non-projective) compact Kähler manifolds admitting holomorphic vector fields. As a main result we show that existence of a constant scalar curvature Kähler (cscK) metric implies geodesic K-polystability, in a sense that is expected to be equivalent to K-polystability in general. In particular, in the spirit of an expectation of Chen–Tang [28] we show that geodesic K-polystability implies algebraic K-polystability for polarized manifolds, so our main result recovers a possibly stronger version of results of Berman–Darvas–Lu

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Zilioti, G. J. M., R. C. Santos, and J. A. S. Lima. "From de Sitter to de Sitter: Decaying Vacuum Models as a Possible Solution to the Main Cosmological Problems." Advances in High Energy Physics 2018 (August 16, 2018): 1–7. http://dx.doi.org/10.1155/2018/6980486.

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Decaying vacuum cosmological models evolving smoothly between two extreme (very early and late time) de Sitter phases are able to solve or at least to alleviate some cosmological puzzles; among them we have (i) the singularity, (ii) horizon, (iii) graceful-exit from inflation, and (iv) the baryogenesis problem. Our basic aim here is to discuss how the coincidence problem based on a large class of running vacuum cosmologies evolving from de Sitter to de Sitter can also be mollified. It is also argued that even the cosmological constant problem becomes less severe provided that the characteristi

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Honda, Shouhei. "Bakry-Émery Conditions on Almost Smooth Metric Measure Spaces." Analysis and Geometry in Metric Spaces 6, no. 1 (2018): 129–45. http://dx.doi.org/10.1515/agms-2018-0007.

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Abstract In this short note, we give a sufficient condition for almost smooth compact metric measure spaces to satisfy the Bakry-Émery condition BE(K, N). The sufficient condition is satisfied for the glued space of any two (not necessary same dimensional) closed pointed Riemannian manifolds at their base points. This tells us that the BE condition is strictly weaker than the RCD condition even in this setting, and that the local dimension is not constant even if the space satisfies the BE condition with the coincidence between the induced distance by the Cheeger energy and the original distan

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Bolognesi, S. "A cosmology of a trans-Planckian theory and dark energy." International Journal of Modern Physics D 23, no. 05 (2014): 1450046. http://dx.doi.org/10.1142/s0218271814500461.

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We investigate a model based on a generalized version of the Fourier transform for curved spacetime manifolds. This model is possible if the metric has an asymptotic flat region which allows a duality to be implement between coordinates and momenta, hence, the model's name, trans-Planckian. The theory and the action are based on the postulate of the absolute egalitarian relation between coordinates x and momenta p. We show how to implement this construction in a cosmological setting, on a Friedman–Robertson–Walker (FRW) metric background, where the asymptotic time infinity plays the role of th

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You, Yuncheng. "Inertial manifolds and stabilization of nonlinear beam equations with Balakrishnan-Taylor damping." Abstract and Applied Analysis 1, no. 1 (1996): 83–102. http://dx.doi.org/10.1155/s1085337596000048.

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In this paper we study a hinged, extensible, and elastic nonlinear beam equation with structural damping and Balakrishnan-Taylor damping with the full exponent2(n+β)+1. This strongly nonlinear equation, initially proposed by Balakrishnan and Taylor in 1989, is a very general and useful model for large aerospace structures. In this work, the existence of global solutions and the existence of absorbing sets in the energy space are proved. For this equation, the feature is that the exponential rate of the absorbing property is not a global constant, but which is uniform for the family of trajecto

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Davis, Simon. "The quantum consistency of the 12-dimensional theory." International Journal of Modern Physics A 31, no. 04n05 (2016): 1650010. http://dx.doi.org/10.1142/s0217751x1650010x.

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By considering the 12-dimensional superalgebra, inferences are drawn about the finiteness of the 12-dimensional theory unifying the superstring models. The dimensional reduction of the nonsupersymmetric theory in four dimensions to a supersymmetric action in three dimensions is established for the bosonic sector. It is found to be the quotient by [Formula: see text] of the integration over the fiber coordinate of a theory with [Formula: see text] supersymmetry. Consequently, a flow on the moduli space of Spin(7) manifolds from a [Formula: see text] structure with [Formula: see text] supersymme

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KIFER, YURI. "STOCHASTIC VERSIONS OF ANOSOV'S AND NEISTADT'S THEOREMS ON AVERAGING." Stochastics and Dynamics 01, no. 01 (2001): 1–21. http://dx.doi.org/10.1142/s0219493701000023.

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In systems which combine slow and fast motions the averaging principle says that a good approximation of the slow motion can be obtained by averaging its parameters in fast variables. This setup arises, for instance, in perturbations of Hamiltonian systems where motions on constant energy manifolds are fast and across them are slow. When these perturbations are deterministic Anosov's theorem says that the averaging principle works except for a small in measure set of initial conditions while Neistadt's theorem gives error estimates in the case of perturbations of integrable Hamiltonian systems

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TSOUPROS, GEORGE. "CONFORMAL ANOMALIES FOR INTERACTING SCALAR FIELDS ON CURVED MANIFOLDS WITH BOUNDARY." International Journal of Modern Physics A 20, no. 05 (2005): 1027–64. http://dx.doi.org/10.1142/s0217751x05020884.

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The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit calculations are given for those contributions to the conformal anomaly which emerge as a result of free scalar propagation as well as from scalar self-interactions up to second order in the scalar self-coupling. The renormalization-group behavior of the theory is, subsequently, exploited in order to advance the evaluation of the conformal anomaly to third order in

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HO, CHOON-LIN. "CONSTANT GAUGE FIELDS AND SYMMETRY BREAKING ON TORUS." Modern Physics Letters A 05, no. 25 (1990): 2021–29. http://dx.doi.org/10.1142/s0217732390002304.

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We examine symmetry breaking in an SU(2) gauge theory with a massless fermion defined on space-time manifold R1, d−3 × T2. Vacuum gauge field configuration is taken to have a constant field strength on the torus. Effective Potential in this background is evaluated and compared with that of pure gauge vacuum configuration. It is found that, in d ≡ 5, 7 (mod 8), vacuum with sufficiently large color magnetic flux on the torus could have lower energy density. This result applies to a U(1) theory as well. For SU(2) theory, the symmetry is broken to U(1).

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Palumbo, Giandomenico. "Gravitational behavior of an effective topological field theory in a gravitational instanton background." Modern Physics Letters A 31, no. 02 (2016): 1650015. http://dx.doi.org/10.1142/s0217732316500152.

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Effective topological field theories describe the properties of Dirac fermions in the low-energy regime. In this work, we introduce a new emergent gravity model by considering Dirac fermions invariant under local de Sitter transformations in four-dimensional open manifolds. In the context of Cartan geometry, fermions couple to spacetime through a Spin(5) Cartan connection that can be decomposed in spin connection and tetrads. In presence of a gravitational instanton background, we show that the corresponding effective topological field theory becomes a dynamical gravitational theory with a pos

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Belta, Calin, and Vijay Kumar. "Optimal Motion Generation for Groups of Robots: A Geometric Approach." Journal of Mechanical Design 126, no. 1 (2004): 63–70. http://dx.doi.org/10.1115/1.1641190.

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In this paper we generate optimal smooth trajectories for a set of fully-actuated mobile robots. Given two end configurations, by tuning one parameter, the user can choose an interpolating trajectory from a continuum of curves varying from that corresponding to maintaining a rigid formation to motion of the robots toward each other. The idea behind our method is to change the original constant kinetic energy metric in the configuration space and can be summarized into three steps. First, the energy of the motion as a rigid structure is decoupled from the energy of motion along directions that

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BRATCHIKOV, A. V. "RENORMALIZATION PROPERTIES OF TWO-DIMENSIONAL HOMOGENEOUS SYMPLECTIC σ-MODELS". Modern Physics Letters A 07, № 24 (1992): 2229–33. http://dx.doi.org/10.1142/s0217732392001993.

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The structure of renormalization of the two-dimensional σ-model, built on an arbitrary homogeneous symplectic manifold, is found within a convenient parametrization of the fields. Solution of the Ward-Takahashi (WT) identities determines the renormalized action up to a finite number of renormalization constants. All the infinities can be absorbed in a coupling constants renormalization and in a renormalization of an auxiliary constant finite-dimensional matrix.

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Bravetti, Alessandro, and Orlando Luongo. "Dark energy from geometrothermodynamics." International Journal of Geometric Methods in Modern Physics 11, no. 08 (2014): 1450071. http://dx.doi.org/10.1142/s0219887814500716.

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We investigate a general class of equations of state reproducing the dark energy effects in terms of geometric considerations on thermodynamic interaction. We infer cosmological solutions by combining thermodynamics with contact manifold and Riemannian geometry, showing that the standard ΛCDM model can be treated as a limiting case of a more general approach, providing early time departures as the universe expands. Thus, we interpret the microscopic nature of dark energy through the mathematical formalism of geometrothermodynamics (GTD). In particular, we investigate the thermodynamic nature o

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Choi, Gundon, and Gabjin Yun. "Harmonic morphisms and subharmonic functions." International Journal of Mathematics and Mathematical Sciences 2005, no. 3 (2005): 383–91. http://dx.doi.org/10.1155/ijmms.2005.383.

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LetMbe a complete Riemannian manifold andNa complete noncompact Riemannian manifold. Letϕ:M→Nbe a surjective harmonic morphism. We prove that ifNadmits a subharmonic function with finite Dirichlet integral which is not harmonic, andϕhas finite energy, thenϕis a constant map. Similarly, iffis a subharmonic function onNwhich is not harmonic and such that|df|is bounded, and if∫M|dϕ|<∞, thenϕis a constant map. We also show that ifNm(m≥3)has at least two ends of infinite volume satisfying the Sobolev inequality or positivity of the first eigenvalue of the Laplacian, then there are no nonconstant

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Cotăescu, Ion I. "Time evolution of the free Dirac field in spatially flat FLRW space–times." International Journal of Modern Physics A 35, no. 32 (2020): 2030019. http://dx.doi.org/10.1142/s0217751x20300197.

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The framework of the relativistic quantum mechanics on spatially flat FLRW space–times is considered for deriving the analytical solutions of the Dirac equation in different local charts of these manifolds. Systems of commuting conserved operators are used for determining the fundamental solutions as common eigenspinors giving thus physical meaning to the integration constants related to the eigenvalues of these operators. Since these systems, in general, are incomplete on the FLRW space–times there are integration constants that must be fixed by setting the vacuum either as the traditional ad

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MISRA, AALOK. "MQCD, ("BARELY") G2 MANIFOLDS AND (ORIENTIFOLD OF) A COMPACT CALABI–YAU." International Journal of Modern Physics A 20, no. 10 (2005): 2059–97. http://dx.doi.org/10.1142/s0217751x05021075.

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We begin with a discussion on two apparently disconnected topics — one related to nonperturbative superpotential generated from wrapping an M2-brane around a supersymmetric three cycle embedded in a G2-manifold evaluated by the path-integral inside a path-integral approach of Ref. 1, and the other centered around the compact Calabi–Yau CY3(3, 243) expressed as a blow-up of a degree-24 Fermat hypersurface in WCP4[1, 1, 2, 8, 12]. For the former, we compare the results with the ones of Witten on heterotic worldsheet instantons.2 The subtopics covered in the latter include an 𝒩=1 triality between

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BALACHANDRAN, A. P., and S. VAIDYA. "INSTANTONS AND CHIRAL ANOMALY IN FUZZY PHYSICS." International Journal of Modern Physics A 16, no. 01 (2001): 17–39. http://dx.doi.org/10.1142/s0217751x01003214.

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In continuum physics, there are important topological aspects like instantons, θ-terms and the axial anomaly. Conventional lattice discretizations often have difficulties in treating one or the other of these aspects. In this paper, we develop discrete quantum field theories on fuzzy manifolds using noncommutative geometry. Basing ourselves on previous treatments of instantons and chiral fermions (without fermion doubling) on fuzzy spaces and especially fuzzy spheres, we present discrete representations of θ-terms and topological susceptibility for gauge theories and derive axial anomaly on th

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NISHINO, HITOSHI. "DOES HETEROTIC STRING GENERATE CHERN-SIMONS ACTION IN THREE DIMENSIONS?" Modern Physics Letters A 07, no. 20 (1992): 1805–15. http://dx.doi.org/10.1142/s0217732392001518.

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We study the possibility that the ten-dimensional (D=10) heterotic superstring generates a class of Chern-Simons theories in three dimensions, via compactifications on the internal seven-dimensional manifolds. We give an explicit example of such compactifications on (Calabi-Yau)6×S1×(Mink.)3, using the dual formulation of the heterotic string. The string tension 1/α′ as well as the Yang-Mills coupling constant g2 in D=10 is double-quantized in terms of two integers, through a condensate of the antisymmetric field strength NM1…M7, which is dual to the ordinary field strength GMNP. The resultant

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GONZÁLEZ-FERNÁNDEZ, B., and A. CAMACHO. "FLUID-GRAVITY CORRESPONDENCE UNDER THE PRESENCE OF VISCOSITY." Modern Physics Letters A 27, no. 32 (2012): 1250185. http://dx.doi.org/10.1142/s0217732312501854.

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This work addresses the analogy between the speed of sound of a viscous, barotropic, and irrotational fluid and the equation of motion for a non-massive field in a curved manifold. It will be shown that the presence of viscosity implies the introduction, into the equation of motion of the gravitational analogue, of a source term which entails the flow of energy from the non-massive field to the curvature of the spacetime manifold. The stress–energy tensor is also computed and it is found not to be constant, which is consistent with such energy interchange.

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AGISHTEIN, M. E., and A. A. MIGDAL. "SIMULATIONS OF FOUR-DIMENSIONAL SIMPLICIAL QUANTUM GRAVITY AS DYNAMICAL TRIANGULATION." Modern Physics Letters A 07, no. 12 (1992): 1039–61. http://dx.doi.org/10.1142/s0217732392000938.

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Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. We studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: we reached about 5×104 simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model sh

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CARFORA, M., and A. MARZUOLI. "REIDEMEISTER TORSION AND SIMPLICIAL QUANTUM GRAVITY." International Journal of Modern Physics A 08, no. 11 (1993): 1933–80. http://dx.doi.org/10.1142/s0217751x93000813.

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We show that three-dimensional simplicial quantum gravity, as described by dynamically triangulated manifolds, is connected with a Gaussian model determined by the simple homotopy types of the underlying manifolds. By exploiting this result it is shown that the partition function of three-dimensional simplicial quantum gravity is well defined in a convex region in the plane of the gravitational and cosmological coupling constants. Such a region is determined by the Reidemeister–Franz torsion invariants associated with orthogonal representations of the fundamental groups of the set of manifolds

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LIM, ADRIAN P. C. "PATH INTEGRALS ON A COMPACT MANIFOLD WITH NON-NEGATIVE CURVATURE." Reviews in Mathematical Physics 19, no. 09 (2007): 967–1044. http://dx.doi.org/10.1142/s0129055x07003164.

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A typical path integral on a manifold, M is an informal expression of the form [Formula: see text] where H(M) is a Hilbert manifold of paths with energy E(σ) < ∞, f is a real-valued function on H(M), [Formula: see text] is a "Lebesgue measure" and Z is a normalization constant. For a compact Riemannian manifold M, we wish to interpret [Formula: see text] as a Riemannian "volume form" over H(M), equipped with its natural G1 metric. Given an equally spaced partition, [Formula: see text] of [0, τ], let [Formula: see text] be the finite dimensional Riemannian submanifold of H(M) consisting of p

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Cardenas, Ivan A., and Anton A. Lipovka. "Variation of the fine-structure constant caused by expansion of the Universe." Modern Physics Letters A 34, no. 38 (2019): 1950315. http://dx.doi.org/10.1142/s0217732319503152.

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In this paper, we evaluate the fine-structure constant variation that should take place as the pseudo-Riemannian Universe expands and its curvature is changed adiabatically. Such variation of the fine-structure constant is attributed to an energy loss by an extended physical system (consisting of baryonic component and electromagnetic (EM) field) due to expansion of our Universe. Obtained ratio [Formula: see text] (per second) is only five times smaller than actually reported experimental limit on this value. For this reason, the obtained variation can probably be measured within a couple of y

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Smoller, Joel, Blake Temple, and Zeke Vogler. "An instability of the standard model of cosmology creates the anomalous acceleration without dark energy." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2207 (2017): 20160887. http://dx.doi.org/10.1098/rspa.2016.0887.

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We identify the condition for smoothness at the centre of spherically symmetric solutions of Einstein’s original equations without the cosmological constant or dark energy. We use this to derive a universal phase portrait which describes general, smooth, spherically symmetric solutions near the centre of symmetry when the pressure p =0. In this phase portrait, the critical k =0 Friedmann space–time appears as a saddle rest point which is unstable to spherical perturbations. This raises the question as to whether the Friedmann space–time is observable by redshift versus luminosity measurements

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