Magnetic fields and factored two-spheres

Abstract

A magnetic monopole is placed at the centre of a 3-ball whose surface, S, is tiled by the symmetry group, G, of a regular solid. The quantum mechanics on the two-dimensional quotient, S/G, is developed and the monopole charge is found to be quantized in the expected manner. The heat-kernels and zeta-functions are evaluated and the Casimir energies computed as examples of the formalism. Numerical approaches to the calculation of the derivative of the Barnes zeta-function are presented.

43 pages, 4 figures. Uses JyTeX

References in corpus (1)

• Bose-Einstein condensation in arbitrarily shaped cavities

Cited by in corpus (5)

• Warped Brane Worlds in Six Dimensional Supergravity
• The Barnes zeta-function, sphere determinants and Glaisher- Kinkelin-Bendersky constants
• Spectral analysis and zeta determinant on the deformed spheres
• Spherical Universe topology and the Casimir effect
• p-forms on d-spherical tessellations