Unitary Representations of the Homogeneous Lorentz Group in an O(1,1) O(2) Basis and Some Applications to Relativistic Equations

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Unitary Representations of the Homogeneous Lorentz Group in an O(1,1) O(2) Basis and Some Applications to Relativistic Equations

Kalnins, Ernie G.

Identifier: http://hdl.handle.net/10289/1252

Date: 1972

Type: Journal Article

Citation: Kalnins, E.G. (1972). Unitary Representations of the Homogeneous Lorentz Group in an O(1,1) O(2) Basis and Some Applications to Relativistic Equations. Journal of Mathematical Physics, 13, 1304.

Rights: Copyright 1972 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jsp

Abstract:

Unitary irreducible representations of the homogeneous Lorentz group O(3, 1) belonging to the principal series are reduced with respect to the subgroup O(1,1) O(2). As an application we determine the mixed basis matrix elements between O(3) and O(1,1) O(2) bases and derive recurrence relations for them. This set of functions is then used to obtain invariant expansions of solutions of the Dirac and Proca free field equations. These expansions are shown to have the correct nonrelativistic limit.

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