2003/10/16 by Subir Ghosh, Ghosh, Subir
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0310155
12 pages, Latex, modified version, no change in maths. part, to appear in Mod.Phys.Lett.A
openalex publication_date 2003/10/16 · arxiv created 2004/06/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study space-time symmetries in Non-Commutative (NC) gauge theory in the (constrained) Hamiltonian framework. The specific example of NC CP(1) model, posited in \citesg, has been considered. Subtle features of Lorentz invariance violation in NC field theory were pointed out in \citehar. Out of the two - Observer and Particle - distinct types of Lorentz transformations, symmetry under the former, (due to the translation invariance), is reflected in the conservation of energy and momentum in NC theory. The constant tensor θμν (the noncommutativity parameter) destroys invariance under the latter. In this paper we have constructed the Hamiltonian and momentum operators which are the generators of time and space translations respectively. This is related to the Observer Lorentz invariance. We have also shown that the Schwinger condition and subsequently the Poincare algebra is not obeyed and that one can not derive a Lorentz covariant dynamical field equation. These features signal a loss of the Particle Lorentz symmetry. The basic observations in the present work will be relevant in the Hamiltonian study of a generic noncommutative field theory.