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Composite parameterization and Haar measure for unitary groups

Christoph Spengler
Organization: University of Vienna
Department: Faculty of Physics
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Implementations of the composite parameterization for the unitary group U(d) and special unitary group SU(d) of arbitrary dimension d. The present mathematica files also yield the associated (normalized) Haar measures on U(d) and SU(d), as well as the exact parameter ranges.

Possible applications: Optimization problems and group integrals over U(d) and SU(d).

For details on the parameterization and the corresponding Haar measure see the references: and

*Science > Physics > Quantum Physics

optimization, parameterization, Haar measure, group integrals, quantum information, quantum mechanics, quantum physics, special unitary group, special unitary matrices, unitary group, unitary matrices, U(N), SU(N)
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compositeSU.nb (28.6 KB) - Mathematica Notebook [for Mathematica 8.0]
compositeU.nb (24.5 KB) - Mathematica Notebook [for Mathematica 8.0]