Invariant spinor representations of finite rotation matrices

Authors

N. L. Manakov, Voronezh State UniversityFollow
A. V. Meremianin, Voronezh State UniversityFollow
Anthony F. Starace, University of Nebraska-LincolnFollow

Document Type

Article

Date of this Version

9-1-2001

Comments

Published by American Physical Society. Phys. Rev. A 64, 032105 (2001). http://pra.aps.org. Copyright © 2001 American Physical Society. Permission to use.

Abstract

Our recent results [N. L. Manakov et al., Phys. Rev. A 57, 3233 (1998); 61, 022103 (2000)] on the invariant representations of finite rotation matrices (FRM’s) of integer rank j (in terms of tensor products of vectors connected with a space-fixed reference frame) are generalized here for the general case of arbitrary (i.e., integer or half-integer) rank j. This extension is carried out by using new spinor representations of FRM’s in terms of specially introduced spinor-annihilation operators. We demonstrate that all widely used, standard representations of FRM’s follow as special cases of our invariant representation for particular parametrizations of the rotation parameters. As the simplest application of invariant spinor representations of FRM’s, the factorized form of Wigner d^j (β) matrices with an arbitrary rank j is obtained as a product of two triangular matrices composed of various powers of cos(β/2).