On the paraboson representations of theSp4,R algebra and their reduction with respect to theO3,1 subalgebra View Full Text


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Article Info

DATE

1972-01

AUTHORS

C. Alabiso, F. Duimio

ABSTRACT

In this paper we consider the class of irreducible representations (IR’s) of theSp4,R ∼O3,2 algebra (belonging to the discrete series), which can be constructed in the Hilbert-Fock space of two paraboson oscillators. In the case of order of parastatistics 1 (boson case) the two IR’s of theSp4,R algebra which can be constructed remain irreducible with respect to theO3,1 subalgebra. For any other order of parastatistics, three IR’s of theSp4,R algebra appear and their reduction with respect to theO3,1 subalgebra implies an infinite continuous direct sum of IR’s of the homogeneous Lorentz algebra belonging to the principal series. Particularly, for the order of parastatistics 2, such a decomposition is directly connected with the problem of the diagonalization of a noncompact generator of theO2,1 algebra in the IR’s of the Bargmann discrete series (Dk+). Possible applications of the results to the theory of the relativistic equations are indicated. More... »

PAGES

163-179

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02728685

DOI

http://dx.doi.org/10.1007/bf02728685

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1019743583


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