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

Abstract

We apply the coherent state approach to study the noncommutative scalar field theory with ${\varphi }^4$ 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.

15 pages, 2 figures, minor corrections