Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-11-27
Int.J.Mod.Phys. A20 (2005) 2847-2857
Physics
High Energy Physics
High Energy Physics - Theory
Six pages, Revtex4 style, no figures; small typo corrected
Scientific paper
10.1142/S0217751X05020823
We work with $N-$dimensional compact real hyperbolic space $X_{\Gamma}$ with universal covering $M$ and fundamental group $\Gamma$. 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 $\Gamma$ as a discrete subgroup of $G$ acting isometrically on $M$, and we take $X_{\Gamma}$ to be the quotient space by that action: $X_{\Gamma}=\Gamma\backslash M = \Gamma\backslash G/K$. The natural Riemannian structure on $M$ (therefore on $X$) induced by the Killing form of $G$ gives rise to a connection $p-$form Laplacian ${\frak L}_p$ 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 $X_{\Gamma}$. The spectral zeta function related to the operator ${\frak L}_p$, considering only the co-exact 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 fuctions 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.
Bytsenko Andrei
Mendes V. S.
Tort Alexandre C.
No associations
LandOfFree
Thermodynamics of Abelian Gauge Fields in Real Hyperbolic Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Thermodynamics of Abelian Gauge Fields in Real Hyperbolic Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Thermodynamics of Abelian Gauge Fields in Real Hyperbolic Spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-518955