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

TL;DR

This paper demonstrates a method for quantizing the Dirac field with electromagnetic interaction without relying on Poincaré symmetry or causal structure, challenging traditional approaches in quantum field theory.

Contribution

It introduces a canonical quantization approach for electrodynamics that bypasses the need for Poincaré symmetry and causal structure, offering a novel perspective.

Findings

Quantization can be performed without Poincaré symmetry.

Perturbative scattering amplitudes are obtainable without causal structure.

The approach simplifies certain aspects of quantum electrodynamics.

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.