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

Anacleto, M. A.; Nascimento, J. R.; Petrov, A. Yu.

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

Authors

Anacleto, M. A.

Nascimento, J. R.

Petrov, A. Yu.

Description

We apply the coherent state approach to study the noncommutative scalar field theory with $ϕ^4$ 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 $\frac{1}θ$ singularities arise as the noncommutative parameter $θ$ 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