Deformation Quantization of Geometric Quantum Mechanics

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dc.creatorGarcia-Compean, H.
dc.creatorPlebanski, J. F.
dc.creatorPrzanowski, M.
dc.creatorTurrubiates, F. J.
dc.date2001-12-07
dc.date.accessioned2026-07-07T10:53:42Z
dc.date.available2026-07-07T10:53:42Z
dc.descriptionSecond quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schrodinger spinless field is considered. Under the assumption that the phase space of the Schrodinger field is $C^{\infty}$, both, the Weyl-Wigner-Moyal and Berezin deformation quantizations are discussed and compared. Then the geometric quantum mechanics is also quantized using the Berezin method under the assumption that the phase space is $CP^{\infty}$ endowed with the Fubini-Study Kahlerian metric. Finally, the Wigner function for an arbitrary particle state and its evolution equation are obtained. As is shown this new "second quantization" leads to essentially different results than the former one. For instance, each state is an eigenstate of the total number particle operator and the corresponding eigenvalue is always ${1 \over \hbar}$.
dc.description27+1 pages, harvmac file, no figures
dc.identifierhttps://arxiv.org/abs/hep-th/0112049
dc.identifierhttp://arxiv.org/abs/hep-th/0112049
dc.identifierJ.Phys.A35:4301-4320,2002
dc.identifierdoi:10.1088/0305-4470/35/19/311
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185574
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.subjectQuantum Physics
dc.titleDeformation Quantization of Geometric Quantum Mechanics
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