Self-interacting scalar fields on spacetime with compact hyperbolic spatial part

Abstract

We calculate the one-loop effective potential of a self-interacting scalar field on the spacetime of the form ${\mathbb{R}}^2\times H^2/\Gamma$. The Selberg trace formula associated with a co-compact discrete group $\Gamma$ in $PSL(2,\mathbb{R})$ (hyperbolic and elliptic elements only) is used. The closed form for the one-loop unrenormalized and renormalized effective potentials is given. The influence of non-trivial topology on curvature induced phase transitions is also discussed.

11 pages, LaTex, UTF 287

References in corpus (1)

• Vacuum energy on orbifold factors of spheres

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