Generalized Dirac bracket and the role of the Poincar\'e symmetry in the program of canonical quantization of fields 2

Abstract

In this article the methods of canonical analysis and quantization that were reviewed in the first part of the series are applied to the case of the Dirac field in the presence of electromagnetic interaction. It is shown that the quantization of electrodynamics, which begins with a given Lagrangian and ends by perturbative calculation of scattering probability amplitudes, can be performed in the way that does not employ Poincar\'e symmetry of space--time at any stage. Also, the causal structure is not needed.