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Deformed Clifford algebra and supersymmetric quantum mechanics on a phase space with applications in quantum optics
In order to realize supersymmetric quantum mechanics methods on a four
dimensional classical phase-space, the complexified Clifford algebra of this
space is extended by deforming it with the Moyal star-product in composing the
components of Clifford forms. Two isospectral matrix Hamiltonians having a
common bosonic part but different fermionic parts depending on four real-valued
phase space functions are obtained. The Hamiltonians are doubly intertwined via
matrix-valued functions which are divisors of zero in the resulting
Moyal-Clifford algebra. Two illustrative examples corresponding to
Jaynes-Cummings-type models of quantum optics are presented as special cases of
the method. Their spectra, eigen-spinors and Wigner functions as well as their
constants of motion are also obtained within the autonomous framework of
deformation quantization.Comment: 22 pages. published versio