SPACETIME SYMMETRIES IN NONCOMMUTATIVE GAUGE THEORY: A HAMILTONIAN ANALYSIS

Author:

GHOSH SUBIR1

Affiliation:

1. Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India

Abstract

We study spacetime symmetries in noncommutative (NC) gauge theory in the (constrained) Hamiltonian framework. The specific example of NC CP(1) model, posited in Ref. 9, has been considered. Subtle features of Lorentz invariance violation in NC field theory were pointed out in Ref. 13. 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 Poincaré algebra is not obeyed and that one cannot 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Physics and Astronomy,Astronomy and Astrophysics,Nuclear and High Energy Physics

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