Infinite-dimensional representations of the Lsorentz group: The complete series

M. Carmeli, S. Malin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The method used by Carmeli to obtain a new form for the principal series of representations of the group SL(2, C) is further generalized to all completely irreducible (finite and infinite-dimensional) representations of that group. This is done, following Naimark, by extending the meaning of one of the parameters appearing in the formula for the operators of the principal series of representations. As a result a new form for the complete series of representations of the group SL(2, C) is obtained which describes the transformation law of an infinite set of quantities under the group translation in a way which is very similar, but as a generalization, to the way spinors appear in the finite-dimensional case. The finite-dimensional representation is then discussed in details and the relation between the new set of quantities (which becomes finite in this case) and 2-component spinors is found explicitly.

Original languageEnglish
Pages (from-to)145-156
Number of pages12
JournalInternational Journal of Theoretical Physics
Volume9
Issue number3
DOIs
StatePublished - 1 Mar 1974

ASJC Scopus subject areas

  • General Mathematics
  • Physics and Astronomy (miscellaneous)

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