A New Approach to Scalar Field Theory on Noncommutative Space

TL;DR

This paper introduces a novel framework for scalar field theory on noncommutative space, incorporating new commutation relations and explicit first- and second-quantization methods in operator and functional integral form.

Contribution

It presents a new approach to noncommutative scalar field theory with modified commutation relations and explicit quantization procedures.

Findings

Developed a new representation for x_i and p_j

Performed explicit first- and second-quantization

Applied both operator formalism and functional integral methods

Abstract

A new approach to constructing the noncommutative scalar field theory is presented. Not only between x_i and p_j, we impose commutation relations between x_is as well as p_js, and give a new representation of x_i,p_js. We carry out both first- and second-quantization explicitly. The second-quantization is performed in both the operator formalism and the functional integral one.