Abstract
We introduce a discretization procedure for spinorial field theories which takes place within a continuous space-time background. The implications of our discretization scheme at the quantum level is that integration over fermionic degrees of freedom can be performed in a well-defined manner. The result is a regularized determinant which reproduces known properties of the continuum system. We consider both free and coupled, with a set of external gauge fields, models. We compute the trace of the logarithm of the Euclidean Dirac operator, obtained by our integration, in the representation provided by “position” eigenstates in Euclidean space-time. A two-dimensional application shows compliance of our result with both gauge current conservation and the axial anomaly relation. Finally, we discuss the question whether our discretization scheme provides a nonperturbative definition of spinorial field systems.
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