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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:
22E43 Structure and representation of the Lorentz group
22E70 Applications of Lie groups to the sciences; explicit representations
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