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

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

2011-03-17

arxiv.org/abs/1103.3408v3

J. Math. Phys. 53, 013501 (2012)

Physics

Mathematical Physics

28 pages, example and references added, accepted by J. Math. Phys

Scientific paper

10.1063/1.3672064

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.

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