Regularization of the Poisson Bracket in Field Theory

TL;DR

This paper proposes a modification to the Poisson bracket in field theory to eliminate odd contributions, resulting in a form that facilitates quantization and connects to non-commutative spacetime concepts.

Contribution

It introduces a regularization method for the Poisson bracket in field theory, leading to a more accessible form for quantization and linking to non-commutative spacetime frameworks.

Findings

Modified Poisson bracket free of odd contributions

Connection to a version of the energy-momentum tensor

Potential for quantization and non-commutative spacetime applications

Abstract

In field theory the Poisson bracket $\{F, \mathcal{H}\}$ between an arbitrary function $F$ and the system Hamiltonian $\mathcal{H}$ acquires odd contributions. Here a modification is worked out to remove those terms, which leads to a certain version of the energy-momentum tensor. The resulting Poisson bracket is thus more easily accessible for quantization. An outlook hereupon is given, based on a field theoretic alternative to non-commutative spacetime.