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Representations of the Lorentz group and generalization of helicity states. (Russian. English translation) Zbl 0201.58404
Teor. Mat. Fiz. 4, 328-340 (1970); translation in Theor. Math. Phys. 4, No. 3, 867-878 (1970).
Summary: 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 $$\mathcal D$$ 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.

##### MSC:
 2.2e+44 Structure and representation of the Lorentz group 2.2e+71 Applications of Lie groups to the sciences; explicit representations
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