New forms for the representations of the three-dimensional Lorentz group
- 1 February 1973
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 14 (2), 254-258
- https://doi.org/10.1063/1.1666305
Abstract
We present a uniform construction of all the principal series representations of the three‐dimensional Lorentz group with generators constructed in terms of oscillator operators. In all cases, the Hilbert space and a hyperbolic generator have a simple appearance, while the other two generators give rise to nonlocal transformations involving Bessel functions.Keywords
This publication has 8 references indexed in Scilit:
- Matrices of Finite Lorentz Transformations in a Noncompact Basis. I. Discrete Series of O(2, 1)Journal of Mathematical Physics, 1969
- Master Analytic Representation: Reduction of O(2, 1) in an O(1, 1) BasisJournal of Mathematical Physics, 1968
- Matrix elements of representations of non-compact groups in a continuous basisCommunications in Mathematical Physics, 1968
- Unitary Representations of the Group O(2, 1) in an O(1, 1) BasisJournal of Mathematical Physics, 1967
- Infinite-Component Wave Equations with Hydrogenlike Mass SpectraPhysical Review B, 1967
- Complex angular momenta and the groups SU(1, 1) and SU(2)Annals of Physics, 1966
- Relativistic Wave Equations for Particles with Internal Structure and Mass SpectrumProgress of Theoretical Physics Supplement, 1966
- Irreducible Unitary Representations of the Lorentz GroupAnnals of Mathematics, 1947