Dispersion relations for the self-energy in non-commutative field theories

TL;DR

This paper investigates the IR/UV connection in non-commutative field theories using dispersion relations, revealing divergences in the real part of the self-energy despite well-behaved imaginary parts.

Contribution

It provides a detailed analysis of the dispersion relations for the self-energy in non-commutative $\

Findings

Imaginary part of self-energy remains well-behaved as non-commutativity vanishes.

Real part of self-energy diverges due to high energy behavior of dispersion integral.

Highlights the IR/UV mixing phenomena in non-commutative field theories.

Abstract

We study the IR/UV connection in non-commutative $\phi^{3}$ theory as well as in non-commutative QED from the point of view of the dispersion relation for the self-energy. We show that, although the imaginary part of the self-energy is well behaved as the parameter of non-commutativity vanishes, the real part becomes divergent as a consequence of the high energy behavior of the dispersion integral. Some other interesting features that arise from this analysis are also briefly discussed.