We investigate the mass spectrum of a scalar field in a world with latticized and circular continuum space where background fields take a topological configuration. We find that the mass spectrum is related to the characteristic values of Mathieu functions. The gauge symmetry breaking in a similar spacetime is also discussed.

PACS numbers: 04.50.+h, 11.10.Kk, 11.15.Ha, 11.25.Mj