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Projective Systems of Imprimitivity and Applications for the Galilei Group in 1+2 and 1+3 Dimensions
Author(s) -
Grigore D. R.
Publication year - 1996
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190440104
Subject(s) - unitary state , projective test , mathematics , group (periodic table) , unitary group , pure mathematics , computation , projective unitary group , algebra over a field , projective representation , classical group , projective space , collineation , physics , algorithm , lie group , quantum mechanics , political science , law
The study of the projective unitary irreducible representations of the Galilei group (in 1+3 and 1+2 dimensions) is usually done using firstly some group extensions techniques (in this way one is reduced to the study of true unitary representations) and then Mackey induction procedure. In this paper we reobtain these results using a different approach based on the notion of projective systems of imprimitivity due also to Mackey. This extension of the usual Mackey procedure is presented rather extensively and illustrated by detailed computations concerning the classification of the projective unitary irreducible representations.