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Two particle realisation of the Poincare group with interaction

Shaun N Mosley
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Abstract

A relative position 4-vector is constructed for two spin-zero particles. Some advantages of this relative position over Bakamjian-Thomas are pointed out. The centre-of-mass (CM) and relative positions and momenta are an explicit realisation of the so-called non-canonical covariant representation. The Hamiltonian including potential terms is factorised into CM and relative components, the latter is a Lorentz scalar readily evaluated in the CM rest frame when the relative position, momentum are canonical conjugates.

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Shaun N Mosley. 2005-10-03. Two particle realisation of the Poincare group with interaction. https://arxiv.org/abs/physics/0510018

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