Canonical Quantization of Noncommutative Field Theory

TL;DR

This paper introduces a straightforward canonical quantization method for noncommutative field theories, revealing that elementary excitations are bilocal entities in reduced dimensions, and aligns with star-product approaches.

Contribution

It presents a new canonical quantization approach for noncommutative fields and clarifies the nature of excitations and scattering rules in this framework.

Findings

Elementary excitations are bilocal in (n+1)-dimensional space-time.

Derived Feynman rules match star-product methods after redefinitions.

Provides insight into IR/UV connection in noncommutative theories.

Abstract

A simple method to canonically quantize noncommutative field theories is proposed. As a result, the elementary excitations of a (2n+1)-dimensional scalar field theory are shown to be bilocal objects living in an (n+1)-dimensional space-time. Feynman rules for their scattering are derived canonically. They agree, upon suitable redefinitions, with the rules obtained via star-product methods. The IR/UV connection is interpreted within this framework.