Fermionic anomalies in quantum-mechanical relativistic problems

The authors discuss the existence of ambiguities in the quantization of systems with odd Grassmann degrees of freedom, or anomalies of fermionic nature as they call them, which could lead them to an incorrect quantum counterpart. The authors propose in this work a way of avoiding such ambiguities in the case of relativistic mechanics, which consists in including the odd degrees of freedom into a generalization of the momentum, that fully contains the anomalies. The authors consider this generalized momentum as the relevant variable to quantize, mentioning their gauge transformation properties. The results are illustrated with some examples. In particular, the Dirac oscillator as a typical case of the problems is discussed