scholarly journals THERMODYNAMICS OF ABELIAN GAUGE FIELDS IN REAL HYPERBOLIC SPACES

2005 ◽  
Vol 20 (13) ◽  
pp. 2847-2857 ◽  
Author(s):  
A. A. BYTSENKO ◽  
V. S. MENDES ◽  
A. C. TORT
Keyword(s):  
Zeta Function ◽  
Degrees Of Freedom ◽  
Compact Subgroup ◽  
Discrete Subgroup ◽  
Symmetric Tensor ◽  
Universal Covering ◽  
Thermodynamic Quantities ◽  
Tensor Fields ◽  
Abelian Gauge ◽  
Spectral Zeta Function

We work with N-dimensional compact real hyperbolic space XΓ with universal covering M and fundamental group Γ. Therefore, M is the symmetric space G/K, where G = SO 1(N, 1) and K = SO (N) is a maximal compact subgroup of G. We regard Γ as a discrete subgroup of G acting isometrically on M, and we take XΓ to be the quotient space by that action: XΓ = Γ∖M = Γ∖G/K. The natural Riemannian structure on M (therefore on X) induced by the Killing form of G gives rise to a connection p-form Laplacian 𝔏p on the quotient vector bundle (associated with an irreducible representation of K). We study gauge theories based on Abelian p-forms on the real compact hyperbolic manifold XΓ. The spectral zeta function related to the operator 𝔏p, considering only the coexact part of the p-forms and corresponding to the physical degrees of freedom, can be represented by the inverse Mellin transform of the heat kernel. The explicit thermodynamic functions related to skew-symmetric tensor fields are obtained by using the zeta-function regularization and the trace tensor kernel formula (which includes the identity and hyperbolic orbital integrals). Thermodynamic quantities in the high and low temperature expansions are calculated and new entropy/energy ratios established.

STOCHASTIC QUANTIZATION OF ANTISYMMETRIC TENSOR FIELDS

1986 ◽  
Vol 01 (02) ◽  
pp. 111-118 ◽  
Author(s):  
P.A. AMUNDSSEN ◽  
P.H. DAMGAARD ◽  
B.-S. SKAGERSTAM
Keyword(s):  
Stochastic Process ◽  
Initial Data ◽  
Langevin Equation ◽  
Degrees Of Freedom ◽  
Mass Shell ◽  
Symmetric Tensor ◽  
Gauge Fields ◽  
Stochastic Quantization ◽  
Tensor Fields ◽  
Abelian Gauge

We extend the stochastic quantization procedure of Parisi and Wu to the case of anti-symmetric tensor fields of arbitrary rank. It is shown that the correct number of physical degrees of freedom on mass shell is automatically projected out. The gauge degrees of freedom can be buried in the initial data of the Langevin equation describing the stochastic process in analogy with the treatment of Abelian and non-Abelian gauge fields.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

VACUUM ENERGY IN SPHERICAL DOMAINS: WKB AND UNIFORM ASYMPTOTIC EXPANSIONS

1996 ◽  
Vol 11 (22) ◽  
pp. 4129-4146 ◽  
Author(s):  
AUGUST ROMEO
Keyword(s):  
Zeta Function ◽  
Asymptotic Expansions ◽  
Zero Point ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Point Energy ◽  
Dimensional Dependence ◽  
Spherical Domains ◽  
Spectral Zeta Function ◽  
Uniform Asymptotic Expansions

We evaluate the finite part of the regularized zero-point energy for a massless scalar field confined in the interior of a D-dimensional spherical region. While some insight is offered into the dimensional dependence of the WKB approximations by examining the residues of the spectral-zeta-function poles, a mode-sum technique based on an integral representation of the Bessel spectral zeta function is applied with the help of uniform asymptotic expansions (u.a.e.’s).

The topology of symmetric tensor fields

1997 ◽  
Author(s):  
Lambertus Hesselink ◽  
Yingmei Lavin ◽  
Rajesh Batra ◽  
Yuval Levy ◽  
Lambertus Hesselink ◽  
...  
Keyword(s):  
Symmetric Tensor ◽  
Tensor Fields

UNCONSTRAINED HIGHER SPINS IN FOUR DIMENSIONS

2011 ◽  
Vol 08 (03) ◽  
pp. 511-556 ◽  
Author(s):  
GIUSEPPE BANDELLONI
Keyword(s):  
Equations Of Motion ◽  
Symmetric Tensor ◽  
Tensor Fields ◽  
Geometrical Meaning ◽  
Four Dimensions ◽  
Spin Field ◽  
Angular Momenta ◽  
Higher Spin ◽  
Spin Fields ◽  
The Right

The relativistic symmetric tensor fields are, in four dimensions, the right candidates to describe Higher Spin Fields. Their highest spin content is isolated with the aid of covariant conditions, discussed within a group theory framework, in which auxiliary fields remove the lower intrinsic angular momenta sectors. These conditions are embedded within a Lagrangian Quantum Field theory which describes an Higher Spin Field interacting with a Classical background. The model is invariant under a (B.R.S.) symmetric unconstrained tensor extension of the reparametrization symmetry, which include the Fang–Fronsdal algebra in a well defined limit. However, the symmetry setting reveals that the compensator field, which restore the Fang–Fronsdal symmetry of the free equations of motion, is in the existing in the framework and has a relevant geometrical meaning. The Ward identities coming from this symmetry are discussed. Our constraints give the result that the space of the invariant observables is restricted to the ones constructed with the Highest Spin Field content. The quantum extension of the symmetry reveals that no new anomaly is present. The role of the compensator field in this result is fundamental.

scholarly journals First Chern class and holomorphic tensor fields

1980 ◽  
Vol 77 ◽  
pp. 5-11 ◽  
Author(s):  
Shoshichi Kobayashi
Keyword(s):  
Vector Bundle ◽  
Cotangent Bundle ◽  
Symmetric Tensor ◽  
Complex Vector Bundle ◽  
Tensor Fields ◽  
Kaehler Manifold ◽  
Complex Vector ◽  
Tensor Power ◽  
Holomorphic Sections ◽  
First Chern Class

Let M be an n-dimensional compact Kaehler manifold, TM its (holomorphic) tangent bundle and T*M its cotangent bundle. Given a complex vector bundle E over M, we denote its m-th symmetric tensor power by SmE and the space of holomorphic sections of E by Γ(E).

An equilibration-based a posteriori error bound for the biharmonic equation and two finite element methods

2019 ◽  
Vol 40 (2) ◽  
pp. 951-975 ◽  
Author(s):  
Dietrich Braess ◽  
Astrid S Pechstein ◽  
Joachim Schöberl
Keyword(s):  
Error Bound ◽  
Biharmonic Equation ◽  
Moment Tensor ◽  
Galerkin Approximation ◽  
Symmetric Tensor ◽  
Posteriori Error ◽  
A Posteriori ◽  
Tensor Fields ◽  
A Posteriori Error ◽  
The Moment

Abstract We develop an a posteriori error bound for the interior penalty discontinuous Galerkin approximation of the biharmonic equation with continuous finite elements. The error bound is based on the two-energies principle and requires the computation of an equilibrated moment tensor. The natural space for the moment tensor is that of symmetric tensor fields with continuous normal-normal components, and is well-known from the Hellan-Herrmann-Johnson mixed formulation. We propose a construction that is totally local. The procedure can also be applied to the original Hellan–Herrmann–Johnson formulation, which directly provides an equilibrated moment tensor.

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