Journal of Mathematical Physics

Structure results for the Segal quantization of Fermi systems

Franco Gallone, Antonio Sparzani

Published Sep 1, 1982• 1 citation

Abstract

In Segal’s approach to linear Fermi quantum systems, a one particle picture with linear symmetries (e.g., with a linear dynamics) can be quantized very straightforwardly when a complexification is given for the (real linear) one particle picture. We examine how the symmetries that are embodied in the one particle picture can determine the structure of the family of the possible complexifications. Among other results, we prove that if the symmetries can be represented in a suitably irreducible way then the complexification is essentially unique. Also, when the one particle space is a generalization of the one defined by the Dirac equation, we prove that there are many complexifications, and inequivalent too, as they generate inequivalent representations of the canonical anticommutation relations; however, we find two criteria that single out the ’’physical’’ complexification. We use the general results we prove to discuss a few familiar models.

DOI: 10.1063/1.525545

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