Unitary Representations of the Lorentz Group on 4-Vector Manifolds
- 1 April 1966
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 7 (4) , 764-780
- https://doi.org/10.1063/1.1704991
Abstract
A review is presented of irreducible unitary representations of the (3 + 1)‐dimensional restricted Lorentz group on manifolds of time‐, light‐, and spacelike 4‐vectors. In each case a complete set of orthonormal (in the sense of the distribution theory) basis functions is available. The completeness relation for the nontrivial spacelike case is proved in detail. Expansion formulas, Lorentz‐group analogs of the Fourier integral theorem, are given. In particular, expansions of plane‐wave solutions of the Klein‐Gordon equation for − ∞ < m2 < ∞ are worked out as an illustrative example. Possible physical applications are briefly discussed.Keywords
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