Model Tests of Cluster Separability In Relativistic Quantum Mechanics

Details Model Tests of Cluster Separability In Relativistic Quantum Mechanics Model Tests of Cluster Separability In Relativistic Quantum Mechanics

2011-09-29

arxiv.org/abs/1109.6575v1

Physics

Nuclear Physics

Nuclear Theory

11 pages, 17 figures

Scientific paper

A physical theory should have both the properties of relativistic invariance and of cluster separability. A relativistically invariant quantum theory is defined by a dynamical unitary representation of the Poincare group. Cluster separability means that symmetries and conservation laws that hold for a system of particles also hold for isolated subsystems. A standard construction of dynamical unitary representations of the Poincare group solves the problem of adding interactions that preserve the Poincare commutation relations by including kinematically invariant interactions in the Casimir mass operator. The resulting unitary representation of the Poincare group fails to satisfy cluster properties for systems of three or more particles. Cluster separability can be restored by means of a recursive construction using unitary transformations, but implementation is difficult in practice. We examine a simple model of a current operator in a three-particle system in which the required unitary transformations are approximated by the identity operator. The difference between these unitary transformations and the identity provides a measure of the size of corrections needed to restore cluster properties. Our estimates suggest that in models based on nucleon degrees of freedom that the corrections that restore cluster properties are too small to affect calculations of observables.

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