ON THE MODULI SPACE OF WIGNER QUASIPROBABILITY DISTRIBUTIONS FOR TV-DIMENSIONAL QUANTUM SYSTEMS

摘要

A mapping between operators on the Hilbert space of an N-dimensional quantum system and Wigner quasiprobability distributions defined on the symplectic flag manifold is discussed. The Wigner quasiprobability distribution is constructed as a dual pairing between the density matrix and the Stratonovich-Weyl kernel. It is shown that the moduli space of Stratonovich-Weyl kernels is given by the intersection of the coadjoint orbit space of the group SU(iV) and a unit (N - 2)-dimensional sphere. The general considerations are exemplified by a detailed description of the moduli space of 2, 3, and 4-dimensional systems. Bibliography: 30 titles.