2024/02/06 by J. S. Dowker, Dowker, J. S.
Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mechanical and Optical Resonators #Quantum Electrodynamics and Casimir Effect #Radioactive Decay and Measurement Techniques #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2402.04107
openalex publication_date 2024/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.