Inonu-Wigner contractions on a quantum relativistic collective model for single-hadron bound states

Abstract

Two limiting processes are applied to a new collective model for single-hadron bound states which describes the relativistic quantum-mechanical ratator. The first limiting process is defined by the contraction of the Poincare group into the extended Galilei group (the nonrelativistic limit) and the second by the contraction of the de Sitter groupSO(4, 1) into the Poincare group (the elementary limit). In the elementary limit the model describes a structureless quantum relativistic point particle characterized by the irreducible representations of the Poincare group and in the nonrelativistic limit it describes a nonrelativistic rigid rotator characterized by the irreducible representations of the extended Galilei group and whose mass spectrum is supplied by anE(3) spectrum-generating group. It is shown that the Hamilton operator for the quantum relativistic rotator goes into the Hamilton operators for the structureless relativistic point particle and the nonrelativistic rotator in their respective limiting processes.