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Probabilistic interpretation, group contraction and the Galilean limit of relativistic quantum mechanics

1978; Springer Science+Business Media; Volume: 46; Issue: 1 Linguagem: Inglês

10.1007/bf02748635

2037-4895

J. León, M. Quiŕos, J. Ramírez Mittelbrunn,

Advanced Thermodynamics and Statistical Mechanics

The problem of getting the Galilei group as a limit of the Poincaré group has been solved in a rigorous manner. We use the generalized contraction introduced by Doebner and Melsheimer. Good physical reasons are given for keepingE 3 invariant in the contraction procedure, in spite of other attempts made in this direction. Group representations are contracted by using well-defined mathematical methods studied by Mickelsson and Niederle. Ill-defined contracted states do not appear in this way. An intriguing connection between localizability and contraction has energed through this work. Some physical conclusions are associated to this feature.