This article is cited in 7 papers

Representations of the Lorentz group and generalization of helicity states

Ya. A. Smorodinskii, M. Khusar


Abstract: The principal series of unitary representations of the Lorentz group is obtained by complexification of the three-dimensional group of rotations and by the solution of the eigenvalue equation for the Casimir operators. The representation obtained can be expressed simply in terms of $D$ functions (of the first and second kind) of the group of rotations. The harmonic analysis of the functions on the group is discussed. Spherical functions on a two-dimensional complex sphere are constructed.

Received: 07.10.1969

 English version: Theoretical and Mathematical Physics, 1970, 4:3, 867–876

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