Canonical Quantization, Space-Time Noncommutativity and Deformed Symmetries in Field Theory

TL;DR

This paper develops a canonical quantization framework for noncommutative spacetime field theories, revealing how deformed symmetries naturally emerge through a Drinfeld twist, exemplified with a scalar field in 1+1 dimensions.

Contribution

It introduces a method to incorporate noncommutative spacetime into field theories via reparametrization invariance and symplectic structure deformation, leading to automatically twisted symmetry generators.

Findings

Deformed constraints induce Drinfeld twisting of symmetries.

Method demonstrated for scalar fields in 1+1 dimensions.

Framework generalizable to other fields and dimensions.

Abstract

Within the spirit of Dirac's canonical quantization, noncommutative spacetime field theories are introduced by making use of the reparametrization invariance of the action and of an arbitrary non-canonical symplectic structure. This construction implies that the constraints need to be deformed, resulting in an automatic Drinfeld twisting of the generators of the symmetries associated with the reparametrized theory. We illustrate our procedure for the case of a scalar field in 1+1- spacetime dimensions, but it can be readily generalized to arbitrary dimensions and arbitrary types of fields.