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 = SO1(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 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.
We consider gauge theories based on abelian p−forms on real compact hyperbolic spaces. Using the zeta-function regularization method and the trace tensor kernel formula, we determine explicitly an expression for the vacuum energy (Casimir energy) corresponding to skew-symmetric tensor fields. It is shown that the topological component of the Casimir energy for co-exact forms on even-dimensional spaces, associated with the trivial character, is always negative. We infer on the possible cosmological consequences of this result.
We analyze gauge theories based on abelian p−forms in real compact hyperbolic manifolds. The explicit thermodynamic functions associated with skew-symmetric tensor fields are obtained via zeta-function regularization and the trace tensor kernel formula. Thermodynamic quantities in the high-temperature expansions are calculated and the entropy/energy ratios are established.
We calculate the Casimir energy associated with abelian gauge fields in real compact hyperbolic spaces. The cosmological applications of the vacuum energies are briefly considered.
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