Anomalia multiplicativa não-local para férmions no espaço curvo com torção

Abstract

This thesis investigated the appearance of nonlocal multiplicative anomaly in the context of one-loop quantum corrections for the fermionic action in curved space-time with torsion. The non-local multiplicative anomaly was first observed for the vector field and, more recently, for the scalar field. Therefore, a natural sequence is to extend the studies to other theories, in order to gain greater understanding of their nature and to establish the presence or not in these theories. Then we shall obtain the effective action functional and analyze the inherent arbitrariness when composing an operator of second order. From the different possibilities of obtaining this operator, we calculate the nonlocal contribution of the 1-loop effective action associated with each of these possibilities in order to verify the presence of possible discrepancies between the results, which lead to the appearance of the nonlocal multiplicative anomaly. Some generalizations will contribute to obtainingand analyzing the results. Also, some criteria to eliminate any inconsistencies in the results will be investigated in order to ensure the consistency of theory.