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

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.

14 pages, 2 figures, minor corrections

References in corpus (31)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• Gauge Theory on Noncommutative Spaces
• Space-Time Noncommutative Field Theories And Unitarity
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Space/Time Non-Commutativity and Causality
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
• Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R^4
• Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars
• Two-Loop Diagrams in Noncommutative ${\varphi }_4^4$ theory
• Chiral Gauge Anomalies on Noncommutative R^4
• One Loop Renormalizability of Supersymmetric Yang-Mills Theories on Noncommutative Two-Torus
• A Consistent Noncommutative Field Theory: the Wess-Zumino Model
• A note on consistent anomalies in noncommutative YM theories
• Wilsonian Renormalization Group and the Non-Commutative IR/UV Connection
• Noncommutative Field Theory and Spontaneous Symmetry Breaking
• Renormalization of noncommutative Yang-Mills theories: A simple example
• The Noncommutative Supersymmetric Nonlinear Sigma Model
• Noncommutative perturbation in superspace
• The Three-Dimensional Noncommutative Nonlinear Sigma Model in Superspace
• The Higgs Mechanism in Non-commutative Gauge Theories
• Superfield Effective Action in the Noncommutative Wess-Zumino Model
• Noncommutative Gauge Theory, Divergences and Closed Strings
• Attractive Forces Between Electrons in QED${}_3$
• Perturbative BF-Yang-Mills theory on noncommutative R^4
• Gauge theories on noncommutative spaces
• Supersymmetric Dirac-Born-Infeld theory in noncommutative space
• A Note on Consistent Anomalies

Cited by in corpus (10)

• Quantum Field Theory on Noncommutative Spaces
• Perturbative Approach to Higher Derivative Theories with Fermions
• Superfield Effective Action in the Noncommutative Wess-Zumino Model
• Spontaneous Symmetry Breaking in Noncommutative Field Theory
• Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections
• Supersymmetry and Gravity in Noncommutative Field Theories
• Noncommutative Supersymmetric Field Theories
• Some Aspects of Scattering in (Non) Commutative Gauge Theories