Casimir effects on Riemann surfaces

DOI10.1016/S0019-3577(02)90006-6zbMath1027.81026MaRDI QIDQ1866457

Nobushige Kurokawa, Masato Wakayama

Publication date: 21 December 2003

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

zbMATH Keywords

Riemann surfacesSelberg trace formulaheat kernelzeta functionsSelberg zeta functionCasimir energyFuchsian groups of the first kindMellin transform of a theta series

Mathematics Subject Classification ID

Quantum field theory on curved space or space-time backgrounds (81T20) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Riemann surfaces (30F99)

Related Items

A correspondence principle, Equivalence of zeta function technique and Abel–Plana formula in regularizing the Casimir energy of hyper-rectangular cavities, Casimir energy and modularity in higher-dimensional conformal field theories, Zetas and moments of finite group actions., Absolute Frobenius operators, Some developments of the Casimir effect in p-cavity of (D + 1)-dimensional space–time, A NOTE ON SPECTRAL ZETA FUNCTIONS OF QUANTUM GROUPS, Extensions of zeta functions -- examples and a study of the double sine functions, Hierarchy of the Selberg zeta functions

Cites Work

• Zeta functions of Selberg's type associated with homogeneous vector bundles
• On determinants of Laplacians on Riemann surfaces
• Determinants of Laplacians
• Zeta functions of Selberg's type for compact space forms of symmetric spaces of rank one
• A local index theorem for families of \({\bar \partial}\)-operators on punctured Riemann surfaces and a new Kähler metric on their moduli spaces
• Asymptotic behaviour of spectra of compact quotients of certain symmetric spaces
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