Field Theory in Noncommutative Minkowski Superspace

Abstract

There is much discussion of scenarios where the space-time coordinates x^μare noncommutative. The discussion has been extended to include nontrivial anticommutation relations among spinor coordinates in superspace. A number of authors have studied field theoretical consequences of the deformation of N=1 superspace arising from nonanticommutativity of coordinates θ, while leaving \bar{theta}'s anticommuting. This is possible in Euclidean superspace only. In this note we present a way to extend the discussion by making both θand \bar{theta} coordinates non-anticommuting in Minkowski superspace. We present a consistent algebra for the supercoordinates, find a star-product, and give the Wess-Zumino Lagrangian L_{WZ} within our model. It has two extra terms due to non(anti)commutativity. The Lagrangian in Minkowski superspace is always manifestly Hermitian and for L_{WZ} it preserves Lorentz invariance.

8 pages, added references, two-column format, published in PRD

References in corpus (42)

• String Theory and Noncommutative Geometry
• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Noncommutative Field Theory and Lorentz Violation
• Gravity coupled with matter and foundation of non-commutative geometry
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• Limit on Lorentz and CPT Violation of the Neutron Using a Two-Species Noble-Gas Maser
• Noncommutative Geometry From Strings and Branes
• Non-commutative superspace from string theory
• Noncommutative Superspace, N=1/2 Supersymmetry, Field Theory and String Theory
• Low-energy Limits on the Antisymmetric Tensor Field Background on the Brane and on the Non-commutative Scale
• Non(anti)commutative Superspace
• Review of the Phenomenology of Noncommutative Geometry
• Bounding Noncommutative QCD
• Comments on Non-Commutative Phenomenology
• Some Aspects of Deformations of Supersymmetric Field Theories
• Dirac Quantization of Open Strings and Noncommutativity in Branes
• Superstrings in Graviphoton Background and N=1/2+3/2 Supersymmetry
• Supersymmetric Gauge Theories on Noncommutative Superspace
• Noncommutative Gauge Theory without Lorentz Violation
• N=1/2 Wess-Zumino model is renormalizable
• Two-loop Renormalization for Nonanticommutative N=1/2 Supersymmetric WZ Model
• Supersymmetry in noncommutative superspaces
• Noncommutative field theory and violation of translation invariance
• Supersymmetric Noncommutative QED and Lorentz Violation
• Wilsonian Proof for Renormalizability of N=1/2 Supersymmetric Field Theories
• Lorentz-Invariant Non-Commutative Space-Time Based On DFR Algebra
• CP violation from noncommutative geometry
• Phenomenology of Lorentz-Conserving Noncommutative QED
• Lorentz Invariance And Unitarity Problem In Non-Commutative Field Theory
• Parton Model in Lorentz Invariant Non-Commutative Space
• Lorentz-Invariant Non-Commutative QED
• Superfield theory and supermatrix model
• Deformed N=1 supersymmetry
• N=1/2 Super Yang-Mills Theory on Euclidean AdS2xS2
• Phenomenology of Noncommutative Field Theories
• Discrete Symmetries In Lorentz-Invariant Non-Commutative QED
• A New Gauge-Invariant Regularization Scheme Based on Lorentz-Invariant Noncommutative Quantum Field Theory
• Evaluating matrix elements relevant to some Lorenz violating operators
• Phenomenology of Non-Commutative Field Theories
• New Clock Comparison Tests of Lorentz Symmetry
• Noncommutative Regularization In Gauge Theories

Cited by in corpus (14)

• Lorentz Conserving Noncommutative Standard Model
• On nonanticommutative N=2 sigma-models in two dimensions
• Non-local Wess-Zumino Model on Nilpotent Noncommutative Superspace
• Gauged Wess-Zumino Model in Noncommutative Minkowski Superspace
• Laboratory bounds on Lorentz symmetry violation in low energy neutrino physics
• Cryptoreality of nonanticommutative Hamiltonians
• Chiral Models in Noncommutative N=1/2 Four Dimensional Superspace
• Baryon asymmetry in the Universe resulting from Lorentz violation
• Lorentz-violating dynamics in the pre-Planckian Universe
• Black hole evaporation within a momentum-dependent metric
• CPT-violating neutrino oscillations
• Non-anticommutative Supersymmetric Field Theory and Quantum Shift
• Deriving Spin within a discrete-time theory
• N=1/2 Global SUSY: R-Matrix Approach