Noncommutative and Non-Anticommutative Quantum Field Theory

TL;DR

This paper formulates a quantum field theory in superspace with noncommutative and non-anticommutative coordinates, demonstrating finiteness of one-loop diagrams due to a Gaussian damping factor.

Contribution

It introduces a novel superspace framework with noncommutative and non-anticommutative relations and analyzes a scalar field theory showing finiteness at one loop.

Findings

One-loop diagrams are finite due to Gaussian damping.

The theory incorporates noncommutative and non-anticommutative algebraic structures.

Perturbative analysis confirms improved ultraviolet behavior.

Abstract

A noncommutative and non-anticommutative quantum field theory is formulated in a superspace, in which the superspace coordinates satisfy noncommutative and non-anticommutative relations. A perturbative scalar field theory is investigated in which only the non-anticommutative algebraic structure is kept, and one loop diagrams are calculated and found to be finite due to the damping caused by a Gaussian factor in the propagator.