Field Theory with Coordinate Dependent Noncommutativity

Abstract

We discuss the formulation of classical field theoretical models on $n$-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field theories in noncommutative space-time to obtain local conservation laws (for the electric charge and for the energy-momentum tensor of free fields) and more generally an energy-momentum balance equation for interacting fields. For free field models an analogy with the damped harmonic oscillator in classical mechanics is pointed out, which allows us to get a physical understanding for the obtained conservation laws. To conclude, the formulation of field theories on curved noncommutative space is addressed.

Dedicated to the memory of Manfred Schweda who initiated this work, V2: References added. V3: Comments on the symmetries underlying the conservation laws added, V4: Published version

References in corpus (18)

• A Gravity Theory on Noncommutative Spaces
• Symmetry, Gravity and Noncommutativity
• Hamiltonian dynamics on the symplectic extended phase space for autonomous and non-autonomous systems
• Type III and spectral triples
• Position-dependent noncommutativity in quantum mechanics
• Magnetic fields in noncommutative quantum mechanics
• A-branes and Noncommutative Geometry
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• Noncommutative Geometries and Gravity
• On the $\star$-product quantization and the Duflo map in three dimensions
• Local index formula and twisted spectral triples
• Field Theory on Curved Noncommutative Spacetimes
• On the energy-momentum tensor in Moyal space
• Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• Bootstrapping Non-commutative Gauge Theories from L${}_{\infty }$ algebras
• Semiquantisation Functor and Poisson-Riemannian Geometry, I
• Renormalization and Induced Gauge Action on a Noncommutative Space

Cited by in corpus (2)

• Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
• Quantization of Length in Spaces with Position-Dependent Noncommutativity