Space-time noncommutativity with a bifermionic parameter

Abstract

We consider a Moyal plane and propose to make the noncommutativity parameter Θ^{μν} bifermionic, i.e., composed of two fermionic (Grassmann odd) parameters. The Moyal product then contains a finite number of derivatives, which allows to avoid difficulties of the standard approach. As an example, we construct a two-dimensional noncommutative field theory model based on the Moyal product with a bifermionic parameter and show that it has a locally conserved energy-momentum tensor. The model has no problems with the canonical quantization and appears to be renormalizable.

8 pages, v2: reference added, v3: misprints corrected

References in corpus (21)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Space-Time Noncommutative Field Theories And Unitarity
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• On the unitarity problem in space/time noncommutative theories
• Two-Loop Diagrams in Noncommutative ${\varphi }_4^4$ theory
• Hamiltonian Formalism for Space-time Non-commutative Theories
• Time-ordered Perturbation Theory on Noncommutative Spacetime II: Unitarity
• Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories
• A Canonical Formalism For Lagrangians With Nonlocality Of Finite Extent
• Unitarity in space-time noncommutative field theories
• Quantum noncommutative gravity in two dimensions
• Path Integral for Space-time Noncommutative Field Theory
• New Pseudoclassical model for Weyl particles
• Symmetries and classical quantization
• Stability of a Noncommutative Jackiw-Teitelboim Gravity
• Quantization of pseudoclassical model of spin one relativistic particle
• Canonical Quantization, Space-Time Noncommutativity and Deformed Symmetries in Field Theory
• Constraints, gauge symmetries, and noncommutative gravity in two dimensions

Cited by in corpus (3)

• On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review
• Noncommutativity due to spin
• Nilpotent noncommutativity and renormalization