Composite parameterization and Haar measure for all unitary and special unitary groups

Author(s)
Christoph Spengler, Marcus Huber, Beatrix Hiesmayr
Abstract

We adopt the concept of the composite parameterization of the unitary group U(d) to the special unitary group SU(d). Furthermore, we also consider the Haar measure in terms of the introduced parameters. We show that the well-defined structure of the parameterization leads to a concise formula for the normalized Haar measure on U(d) and SU(d). With regard to possible applications of our results, we consider the computation of high-order integrals over unitary groups.

Organisation(s)
Particle Physics
Journal
Journal of Mathematical Physics
Volume
53
No. of pages
22
ISSN
0022-2488
DOI
https://doi.org/10.1063/1.3672064
Publication date
2012
Peer reviewed
Yes
Austrian Fields of Science 2012
103025 Quantum mechanics
Portal url
https://ucris.univie.ac.at/portal/en/publications/composite-parameterization-and-haar-measure-for-all-unitary-and-special-unitary-groups(2e717b3f-dedb-4354-bf63-a1e8f84c2fe3).html