Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-12-07
J.Phys.A35:4301-4320,2002
Physics
High Energy Physics
High Energy Physics - Theory
27+1 pages, harvmac file, no figures
Scientific paper
10.1088/0305-4470/35/19/311
Second 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 ${1 \over \hbar}$.
García-Compeán Héctor
Plebański Jerzy F.
Przanowski Maciej
Turrubiates Francisco J.
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