Noncommutative Quantization for Noncommutative Field Theory

TL;DR

This paper introduces a novel quantization method for noncommutative field theories that explicitly incorporates noncommutativity during quantization, yet results in correlation functions identical to those of commutative theories, effectively nullifying noncommutative effects.

Contribution

The paper proposes a new quantization procedure for noncommutative field theories that preserves correlation functions and simplifies the incorporation of noncommutativity.

Findings

Correlation functions match those of commutative theories

Noncommutative effects vanish after quantization

Quantization depends explicitly on the noncommutative parameter

Abstract

We present a new procedure for quantizing field theory models on a noncommutative spacetime. The new quantization depends on the noncommutative parameter explicitly and reduces to the canonical quantization in the commutative limit. It is shown that a quantum field theory constructed by the new quantization yeilds exactly the same correlation functions as those of the commutative field theory, that is, the noncommutative effects disappear completely after quantization. This implies, for instance, that by using the new quantization, the noncommutativity can be incorporated in the process of quantization, rahter than in the action as conventionally done.