Generalized Euler Angle Parameterization for U(N) with Applications to SU(N) Coset Volume Measures
arXiv:math-ph/0210057 · doi:10.1016/j.geomphys.2004.03.003
Abstract
In a previous paper (math-ph/0205016) an Euler angle parameterization for SU(N) was given. Here we present a generalized Euler angle parameterization for U(N). The formula for the calculation of the volume for U(N), CP(N) as well as other SU(N) and U(N) cosets will also be given. In addition, the mixed and pure state product measures for N-dimensional density matrices under this parameterization will also be derived.
26 pages, no figures; minor edits, to be published in J. Geom. Phys
References in corpus (8)
- Induced measures in the space of mixed quantum states
- Characterizing the entanglement of symmetric many-particle spin-1/2 systems
- A uniqueness theorem for entanglement measures
- Generalized Euler Angle Paramterization for SU(N)
- A Parametrization of Bipartite Systems Based on SU(4) Euler Angles
- Volumes of Compact Manifolds
- Entanglement Induced Phase Transitions
- Some Applications for an Euler Angle Parameterization of SU(N) and U(N)
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