Towards constructing one-particle representations of the deformed Poincaré algebra

Abstract

We give a method for obtaining states of massive particle representations of the two-parameter deformation of the Poincaré 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 Poincaré 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.

23 pages. New interpretation of the results is given: upon the deformation the rest state of Poincaré algebra is split into an infinite number of states with discrete energy spectrum. Title, abstract and conclusion are changed

References in corpus (6)

• Quantum $\kappa$-Poincare in Any Dimensions
• A New Null-Plane Quantum Poincare Algebra
• Representation Theory of Quantized Poincare Algebra. Tensor Operators and Their Application to One-Partical Systems
• Lorentz Transformations as Lie-Poisson Symmetries
• Lie-Poisson Deformation of the Poincaré Algebra
• Two-parameter deformation of the Poincaré algebra