The low energy limit of the non-commutative Wess-Zumino model

TL;DR

This paper investigates the low energy behavior of the non-commutative Wess-Zumino model, analyzing interaction potentials, nonlocal effects, and unitarity issues in different noncommutativity regimes.

Contribution

It provides a detailed analysis of the non-commutative Wess-Zumino model's low energy limit, including potential derivation, nonlocality, and unitarity considerations.

Findings

Majorana fermions exhibit nonlocal rods orientation in space/space noncommutativity.

Bosons remain unaffected by noncommutativity effects.

Negative time delays indicate nonlocality in scattering waves.

Abstract

The non-commutative Wess-Zumino model is used as a prototype for studying the low energy behaviour of a renormalizable non-commutative field theory. We start by deriving the potential mediating the fermion-fermion and boson-boson interactions in the non-relativistic regime. The quantum counterparts of these potentials are afflicted by irdering ambiguities but we show that there exists an ordering prescription which makes them hermitean. For space/space noncommutativity it turns out that Majorana fermions may be pictured as rods oriented perpendicularly to the direction of motion showing a lack of localituy, while bosons remain insensitive to the effects of noncommutativity. For time/space noncommutativity bosopns and fermions can be regarded as rods oriented along the direction of motion. For both cases of noncommutativity the scattering state described scattered waves, with at least one wave having negative time delay signalizing the underlying nonlocality. The superfield formulation of the model is used to compute the corresponding effective action in the one- and two-loop approximations. In the case of time/space noncommutativity, unitarity is violated in the relativistic regime. However, this does not preclude the existence of the unitary low energy limit.