The Effective Potential in the Noncommutative Field Theories within the Coherent States Approach

TL;DR

This paper uses the coherent state approach to analyze noncommutative scalar field theories, demonstrating ultraviolet finiteness of scattering amplitudes and exploring the behavior of singularities as the noncommutative parameter approaches zero.

Contribution

It introduces a coherent state framework to study noncommutative field theories, revealing finiteness properties and singularity cancellations not seen in traditional approaches.

Findings

Scattering amplitudes are ultraviolet finite in the noncommutative setting.

Singularities appear as the noncommutative parameter tends to zero.

Certain coupling relations cancel singularities, especially in the massless case.

Abstract

We apply the coherent state approach to study the noncommutative scalar field theory with $\phi^4$ self-interaction and Yukawa coupling to the spinor field. We verify that, contrarily to the commutative result, the scattering amplitude is ultraviolet finite. However, the $\frac{1}{\theta}$ singularities arise as the noncommutative parameter $\theta$ tends to zero. For a special relation between two couplings, these singularities are shown to be cancelled, partially in the massive case and totally in the massless case.