English

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

Mathematical Physics 2015-03-19 v3 math.MP Quantum Physics

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.

Keywords

Cite

@article{arxiv.1103.3408,
  title  = {Composite parameterization and Haar measure for all unitary and special unitary groups},
  author = {Christoph Spengler and Marcus Huber and Beatrix C. Hiesmayr},
  journal= {arXiv preprint arXiv:1103.3408},
  year   = {2015}
}

Comments

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