Noncommutative gauge theories and Lorentz symmetry

Abstract

We explicitly derive, following a Noether-like approach, the criteria for preserving Poincare invariance in noncommutative gauge theories. Using these criteria we discuss the various spacetime symmetries in such theories. It is shown that, interpreted appropriately, Poincare invariance holds. The analysis is performed in both the commutative as well as noncommutative descriptions and a compatibility between the two is also established.

LaTeX, 20 pages, slightly improved version, one reference added, version appearing in Phys. Rev. D

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• Topics in Noncommutative Geometry Inspired Physics
• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
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• Tensor Operators in Noncommutative Quantum Mechanics
• Unusual High-Energy Phenomenology of Lorentz-Invariant Noncommutative Field Theories
• Conformal Invariance in noncommutative geometry and mutually interacting Snyder Particles
• On general properties of Lorentz invariant formulation of noncommutative quantum field theory
• Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
• Comment on "Noncommutative gauge theories and Lorentz symmetry, Phys. Rev. D {\bf 70}, 125004 (2004) by R.Banerjee, B.Chakraborty and K.Kumar"
• Noncommutativity in (2+1)-dimensions and the Lorentz group
• Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces
• Some aspects of quantum mechanics and field theory in a Lorentz invariant noncommutative space
• The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space
• Deformed Schrodinger symmetry on noncommutative space
• Classical electrodynamics in a space with spin noncommutativity of coordinates
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Noncommutative geometry induced by spin effects
• Reply to "Comment on 'Noncommutative gauge theories and Lorentz symmetry'"
• Källén-Lehmann representation of noncommutative quantum electrodynamics
• Spontaneous symmetry breaking and masses numerical results in DFR noncommutative space-time
• The standard electroweak model in the noncommutative $DFR$ space-time
• Study on Noncommutative Representations of Galilean Generators
• Energy-momentum non-conservation on noncommutative spacetime and the existence of infinite spacetime dimension
• Theories on noncommutative spaces and deformed symmetries
• Aspects of noncommutativity in field theory, strings and membranes