Noncommutative $\Phi^4$ Theory at Two Loops

TL;DR

This paper investigates the perturbative properties and renormalizability of noncommutative ^4 theory in four dimensions, focusing on two-loop calculations and effective action analysis.

Contribution

It provides a detailed two-loop analysis of noncommutative ^4 theory, including effective action computation and renormalizability assessment.

Findings

Renormalizability of noncommutative ^4 theory up to two loops.

Explicit two-loop effective action calculation.

Discussion of quantization methods for noncommutative field theories.

Abstract

We study perturbative aspects of noncommutative field theories. This work is arranged in two parts. First, we review noncommutative field theories in general and discuss both canonical and path integral quantization methods. In the second part, we consider the particular example of noncommutative $\Phi^4$ theory in four dimensions and work out the corresponding effective action and discuss renormalizability of the theory, up to two loops.