Dynamical noncommutativity and Noether theorem in twisted phi^*4 theory

Abstract

A \star-product is defined via a set of commuting vector fields X_a = e_a^μ(x) \partial_μ, and used in a phi^*4 theory coupled to the e_a^μ(x) fields. The \star-product is dynamical, and the vacuum solution phi =0, e_a^μ(x)=delta_a^μreproduces the usual Moyal product. The action is invariant under rigid translations and Lorentz rotations, and the conserved energy-momentum and angular momentum tensors are explicitly derived.

15 pages LaTeX, minor typos, added references

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• Matrix formulation of superspace on 1D lattice with two supercharges
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• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• UV/IR mixing as a twisted Poincaré anomaly
• Twisted Grosse-Wulkenhaar ${\varphi }^{\star 4}$ model: dynamical noncommutativity and Noether currents
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• $\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory
• Twisted SUSY: twisted symmetry versus renormalizability
• Diffeomorphism-invariant noncommutative gravity with twisted local Lorentz invariance
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• Chern-Simons supergravities, with a twist