ZETA-FUNCTION REGULARIZATION APPROACH TO FINITE TEMPERATURE EFFECTS IN KALUZA-KLEIN SPACE-TIMES

1992 ◽  
Vol 07 (29) ◽  
pp. 2669-2683 ◽  
Author(s):  
ANDREI A. BYTSENKO ◽  
LUCIANO VANZO ◽  
SERGIO ZERBINI
Keyword(s):  
Zeta Function ◽  
Finite Temperature ◽  
Space Time ◽  
Discrete Torsion ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space ◽  
High Temperature Expansion ◽  
Kernel Approach ◽  
The One ◽  
Kaluza Klein

In the framework of heat-kernel approach to zeta-function regularization, the one-loop effective potential at finite temperature for scalar and spinor fields on Kaluza-Klein space-time of the form [Formula: see text], where MP is p-dimensional Minkowski space-time is evaluated. In particular, when the compact manifold is [Formula: see text], the Selberg trace formula associated with discrete torsion-free group Γ of the n-dimensional Lobachevsky space Hn is used. An explicit representation for the thermodynamic potential valid for arbitrary temperature is found. As a result a complete high temperature expansion is presented and the roles of zero modes and topological contributions is discussed.

Spontaneous Compactification Induced by Gravitons and Scalar Field

1997 ◽  
Vol 12 (28) ◽  
pp. 5007-5018
Author(s):  
N. Granda ◽  
E. Loaiza
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Dimensional Sphere ◽  
Minkowski Space Time ◽  
Background Space ◽  
Dimensional Minkowski Space ◽  
The One ◽  
Hilbert Action ◽  
Kaluza Klein ◽  
Made In

We evaluate the one-loop effective potential for the Einstein–Hilbert action coupled to a nonlinear sigma model in a Kaluza–Klein background space M4 × SN (M4 is the four-dimensional Minkowski space–time and SN is the N-dimensional sphere) for odd N. The computation is made in the harmonic and in the light cone gauges. The radius of compactification for some N was found.

MASSLESS SCALAR CASIMIR EFFECT IN A CLASS OF HYPERBOLIC KALUZA-KLEIN SPACE-TIMES

1992 ◽  
Vol 07 (05) ◽  
pp. 397-409 ◽  
Author(s):  
ANDREI A. BYTSENKO ◽  
LUCIANO VANZO ◽  
SERGIO ZERBINI
Keyword(s):  
Casimir Effect ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Torsion Free Group ◽  
Discrete Torsion ◽  
Kernel Approach ◽  
The One ◽  
Comparison Of The Results ◽  
Torsion Free ◽  
Kaluza Klein

In the framework of heat-kernel approach to zeta-function regularization we calculate the one-loop effective potential (Casimir effect) massless scalar field on Kaluza-Klein space-time of the form RD−n×Hn/Γ(2≤n<D). In addition the Selberg trace formula associated with discrete torsion-free group Γ of the n-dimensional Lobachevsky space Hn is used. A negative Casimir effect related to trivial line bundle with character χ=1 is found. A comparison of the results obtained and Casimir effect for massless field on torus backgrounds is also presented.

scholarly journals Elastic shocks in relativistic rigid rods and balls

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180858 ◽  
Author(s):  
João L. Costa ◽  
José Natário
Keyword(s):  
Free Boundary ◽  
Minkowski Space ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Space Time ◽  
Spherically Symmetric ◽  
Soft Phase ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

We study the free boundary problem for the ‘hard phase’ material introduced by Christodoulou in (Christodoulou 1995 Arch. Ration. Mech. Anal. 130 , 343–400), both for rods in (1 + 1)-dimensional Minkowski space–time and for spherically symmetric balls in (3 + 1)-dimensional Minkowski space–time. Unlike Christodoulou, we do not consider a ‘soft phase’, and so we regard this material as an elastic medium, capable of both compression and stretching. We prove that shocks must be null hypersurfaces, and derive the conditions to be satisfied at a free boundary. We solve the equations of motion of the rods explicitly, and we prove existence of solutions to the equations of motion of the spherically symmetric balls for an arbitrarily long (but finite) time, given initial conditions sufficiently close to those for the relaxed ball at rest. In both cases we find that the solutions contain shocks if and only if the pressure or its time derivative do not vanish at the free boundary initially. These shocks interact with the free boundary, causing it to lose regularity.

FINITE TEMPERATURE EFFECTIVE POTENTIAL IN A KALUZA-KLEIN UNIVERSE

1990 ◽  
Vol 05 (02) ◽  
pp. 353-361 ◽  
Author(s):  
PINAKI ROY
Keyword(s):  
Low Temperature ◽  
Effective Potential ◽  
Finite Temperature ◽  
Scalar Fields ◽  
Walker Metric ◽  
The One ◽  
Kaluza Klein

We evaluate the finite temperature one-loop effective potential for scalar fields in Kaluza-Klein universe consisting of the product of a space with open Robertson-Walker metric and the N sphere SN. The one-loop effective potential has been computed in both high and low temperature limits.

A STRING MODEL FOR D-DIMENSIONAL DE SITTER SPACE–TIME AND EQUATIONS OF MOTION

2005 ◽  
Vol 20 (26) ◽  
pp. 6065-6081
Author(s):  
PAUL BRACKEN
Keyword(s):  
Evolution Equations ◽  
Gordon Equation ◽  
Equations Of Motion ◽  
String Model ◽  
De Sitter Space ◽  
Space Time ◽  
System Of Equations ◽  
De Sitter ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

De Sitter space–time is considered to be represented by a D-dimensional hyperboloid embedded in (D+1)-dimensional Minkowski space–time. The string equation is derived from a string action which contains a Lagrange multiplier to restrict coordinates to de Sitter space–time. The string system of equations is equivalent to a type of generalized sinh–Gordon equation. The evolution equations for all the variables including the coordinates and their derivatives are obtained for D=2,3 and 4.

On k-Type 2-Degenerate Slant Helices in 4-Dimensional Minkowski Space-Time

2018 ◽  
Vol 7 (1) ◽  
pp. 147-151 ◽  
Author(s):  
Zühal Küçükarslan Yüzbaşı ◽  
Münevver Yıldırım Yılmaz
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

HOW SINGULAR A SPACE CAN SUPERSTRINGS THREAD?

1991 ◽  
Vol 06 (03) ◽  
pp. 207-216 ◽  
Author(s):  
TRISTAN HÜBSCH
Keyword(s):  
Minkowski Space ◽  
Moduli Space ◽  
Space Time ◽  
3 Dimensional ◽  
Ricci Flat ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

Many superstring models with N=1 supergravity in 4-dimensional Minkowski space-time involve σ-models with complex 3-dimensional, Ricci-flat target manifolds. In general, inclusion of singular target spaces probes the boundary of the moduli space and completes it. Studying suitably singular σ-models, the author found certain criteria for the severity of admissible singularizations.

Zeta-function regularization for Kaluza-Klein finite temperature theories with chemical potentials

1992 ◽  
Vol 291 (1-2) ◽  
pp. 26-31 ◽  
Author(s):  
Andrei A Bytsenko ◽  
Luciano Vanzo ◽  
Sergio Zerbini
Keyword(s):  
Zeta Function ◽  
Finite Temperature ◽  
Chemical Potentials ◽  
Kaluza Klein
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