Mukunda, N.
(1968)
*Unitary representations of the homogeneous Lorentz group in an O(2, 1) basis*
Journal of Mathematical Physics, 9
(1).
pp. 50-61.
ISSN 0022-2488

Full text not available from this repository.

Official URL: http://link.aip.org/link/jmapaq/v9/i1/p50/s1

Related URL: http://dx.doi.org/10.1063/1.1664476

## Abstract

Unitary irreducible representations of the homogeneous Lorentz group, SO(3, 1), belonging to the principal series and containing integral angular momenta, are reduced with respect to the subgroup SO(2, 1). It is found that the representation {j_{0}, ρ} of SO(3, 1), where j_{0} is a nonnegative integer and ρ a real number, contains each representation of SO(2, 1) of the continuous class (nonexceptional and integral) twice, and each of the discrete representations D_{k}^{(±)} of SO(2, 1) once, for k = 1, 2, ..., j_{0}. The latter representations are absent for j_{0} = 0. It is shown that the basis states of the representation D_{k}^{(±)} (for k ≥ 2) lie in the domain of those generators of SO(3, 1) that are outside the SO(2, 1) subalgebra, while the states of the representations D_{1}^{(±)} do not lie in this domain. It is further shown that from the point of view of the nature of this domain, the representations D_{1}^{(±)} of SO(2, 1) are very intimately connected to the continuous class representations of SO(2, 1), and that these two discrete representations act as a bridge between the remaining discrete representations on the one hand, and the continuous class representations on the other.

Item Type: | Article |
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Source: | Copyright of this article belongs to American Institute of Physics. |

ID Code: | 25347 |

Deposited On: | 06 Dec 2010 13:32 |

Last Modified: | 08 Jun 2011 05:29 |

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