Higher Derivative Operators in the Noncommutative Schwinger Model

TL;DR

This paper investigates the noncommutative Schwinger model, showing that noncommutativity does not alter the Schwinger mass at first order but induces higher derivative kinetic terms, linking non-unitarity to these terms.

Contribution

It demonstrates that noncommutativity leads to higher derivative kinetic terms without modifying the Schwinger mass at first order, providing insights into non-unitarity in noncommutative field theories.

Findings

Schwinger mass remains unchanged at first order in noncommutative parameter.

Higher derivative kinetic terms are generated by vacuum polarization diagrams.

Non-unitarity is characterized by the presence of higher derivative terms.

Abstract

A study of the noncommutative Schwinger model is presented. It is shown that the Schwinger mass is not modified by the noncommutativity of spacetime till the first nontrivial order in the noncommutative parameter. Instead, a higher derivative kinetic term is dynamically generated by the lowest-order vacuum polarization diagrams. We argue that in the framework of the Seiberg-Witten map the feature of non-unitarity for a field theory with space-time noncommutativity is characterized by the presence of higher derivative kinetic terms. The $\theta$-expanded version of a unitary theory will not generate the lowest-order higher derivative quadratic terms.