Galilean symmetry in noncommutative field theory

Abstract

When the interaction potential is suitably reordered, the Moyal field theory admits two types of Galilean symmetries, namely the conventional mass-parameter-centrally-extended one with commuting boosts, but also the two-fold centrally extended ``exotic'' Galilean symmetry, where the commutator of the boosts yields the noncommutative parameter. In the free case, one gets an ``exotic'' two-parameter central extension of the Schroedinger group. The conformal symmetry is, however, broken by the interaction.

arXiv commentCorrected version. Further remarks and references added. LaTex, 8 pages, no figures

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Cited by in corpus (16)

• Non-relativistic conformal symmetries and Newton-Cartan structures
• Aspects of Phase-Space Noncommutative Quantum Mechanics
• Bosons, fermions and anyons in the plane, and supersymmetry
• Space-time symmetry of noncommutative field theory
• Exotic galilean symmetry and non-commutative mechanics
• Super-extended noncommutative Landau problem and conformal symmetry
• A New Type of Conformal Dynamics
• Galilean noncommutative gauge theory: symmetries & vortices
• Path-integral quantization of Galilean Fermi fields
• Nonrelativistic Supersymmetry in Noncommutative Space
• Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces
• Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane
• Symmetries of field theories on the non-commutative plane
• Treating Ostrogradski instability for Gallilean invariant Chern Simon's model via \mathcal{PT} symmetry
• Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions
• Inverse square problem and so(2,1) symmetry in noncommutative space