Towards constructing one-particle representations of the deformed Poincar\'e algebra
Abstract
We give a method for obtaining states of massive particle representations of the two-parameter deformation of the Poincar\'e algebra proposed in q-alg/9601010, q-alg/9505030 and q-alg/9501026. We discuss four procedures to generate eigenstates of a complete set of commuting operators starting from the rest state. One result of this work is the fact that upon deforming to the quantum Poincar\'e algebra the rest state is split into an infinite number of states. Another result is that the energy spectrum of these states is discrete. Some curious residual degeneracy remains: there are states constructed by applying different operators to the rest state which nevertheless are indistinguishable by eigenvalues of all the observables in the algebra.
Keywords
Cite
@article{arxiv.q-alg/9703008,
title = {Towards constructing one-particle representations of the deformed Poincar\'e algebra},
author = {I. Yakushin},
journal= {arXiv preprint arXiv:q-alg/9703008},
year = {2009}
}
Comments
23 pages. New interpretation of the results is given: upon the deformation the rest state of Poincar\'e algebra is split into an infinite number of states with discrete energy spectrum. Title, abstract and conclusion are changed