2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51952We investigate the mass spectrum of a scalar field in a world with latticized and circular continuum space where background fields takes 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.10 pages, 1 eps figure, needs ReVTeX4High Energy Physics - TheoryGeneral Relativity and Quantum CosmologyHigh Energy Physics - PhenomenologyMathematical Physicstext