2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170204This talk presents a study of massless relativistic Dirac fields in three Euclidean dimensions, at finite temperature and density, in the presence of a uniform electromagnetic background. Apart from explaining the behavior of Hall's conductivity for graphene, our results show a direct relationship between the selection of a phase for the Dirac determinant and the generation (or lack thereof) of Berry's phases and Chern-Simons terms.6 pages, 1 figure, to appear in Proceedings of the XIII Conference Selected Problems in Mathematical and Theoretical Physics, Dubna, Russia, June 23-27, 2008High Energy Physics - TheoryMesoscale and Nanoscale PhysicsMathematical Physicstext