×

zbMATH — the first resource for mathematics

Recursive parametrization and invariant phases of unitary matrices. (English) Zbl 1111.81076
Summary: We present further properties of a previously proposed recursive scheme for parametrization of \(n\)-by-\(n\) unitary matrices. We show that the factors in the recursive formula may be introduced in any desired order. The method is used to study the invariant phases of unitary matrices. The case of four-by-four unitary matrices is investigated in detail. We also address the question of how to construct symmetric unitary matrices (i.e., unitary matrices \(U\) that satisfy the condition \(U_{ij}=U_{ji})\) using the recursive approach.

MSC:
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
15A72 Vector and tensor algebra, theory of invariants
22E70 Applications of Lie groups to the sciences; explicit representations
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Gilmore R., Lie Groups, Lie Algebras, and Some of Their Applications (1974) · Zbl 0279.22001
[2] Georgi H., Lie Algebras in Particle Physics: from Isospin to Unified Theories (1982) · Zbl 0505.00036
[3] Dita P., J. Phys. A 36 pp 2871– (2003)
[4] DOI: 10.1016/j.physletb.2004.06.001
[5] DOI: 10.1142/0496
[6] DOI: 10.1016/0370-2693(88)90428-5
[7] DOI: 10.1103/PhysRevD.36.2128
[8] DOI: 10.1016/j.physletb.2005.04.033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.