Ordering problems in fermionic relativistic quantum mechanics

Abstract

We discuss the existence of ambiguities, or anomalies of fermionic nature as we call them, in the quantization of relativistic systems with odd Grassmann degrees of freedom. We propose in this work a way of avoiding such ambiguities in the case of relativistic quantum mechanics, by including the odd degrees of freedom into a generalization of the momentum, in a similar manner to the minimal coupling. We illustrate our results with some examples, including the Dirac oscillator as a typical case of the problems we are dealing with.