Form factors and non-local multiplicative anomaly for fermions with background torsion

We analyse the multiplicative anomaly (MA) in the case of quantized massive fermions coupled to a background torsion. The one-loop effective action (EA) can be expressed in terms of the logarithm of the determinant of the appropriate first-order differential operator acting in the spinors space. Simple algebraic manipulations on determinants must be used in order to apply properly the Schwinger–DeWitt technique, or even the covariant perturbation theory (Barvinsky and Vilkovisky, 1990), which is used in the present work. By this method, we calculate the finite non-local quantum corrections, and analyse explicitly the breakdown of those algebraic manipulations on determinants, called by MA. This feature comes from the finite non-local EA, but does not affect the results in the UV limit, in particular, the beta-functions. Similar results were also obtained in previous papers but for different external fields (QED and scalar field). (paper)