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arXiv · 1411.6048

Time dependent quantum generators for the Galilei group

Gianluigi Filippelli
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Abstract

In 1995 Doebner and Mann introduced an approach to the ray representations of the Galilei group in ($1+1$)-dimensions, giving rise to quantum generators with an explicit dependence on time. Recently (2004) Wawrzycki proposed a generalization of Bargmann's theory: in his paper he introduce phase exponents that are explicitely dependent by 4-space point. In order to find applications of such generalization, we extend the approach of Doebner and Mann to higher dimensions: as a result, we determine the generators of the ray representation in ($2+1$) and ($3+1$) dimensions. The differences of the outcoming formal apparatus with respect to the smaller dimension case are established.

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Gianluigi Filippelli. 2014-11-21. Time dependent quantum generators for the Galilei group. https://doi.org/10.1063/1.3621518

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