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arXiv · 2402.04107

Casimir energy of hyperbolic elements

J. S. Dowker
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Abstract

The contribution, E, of hyperbolic elements to the scalar Casimir energy on a compact quotient of the upper half hyperbolic plane is computed for a propagation operator conformal in three dimensions. Due to the proliferation of prime closed geodesics, the series form for the Casimir energy has an IR divergence. The expression for E is given as a sum of polylogarithms which allows the divergence to be isolated and rendered finite by an {\it ad hoc} Ramanujan renormalisation. The remaining part of E is computed using the specific lower length spectrum of the (2,3,7) triangle and a universal asymptotic form for larger lengths. The tentative value of E found is such as to make the total conformal Casimir energy on the triangle probably negative.

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J. S. Dowker. 2024-02-06. Casimir energy of hyperbolic elements. https://arxiv.org/abs/2402.04107

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