2001/12/07 by H. Garcia-Compean, H García-Compeán, J. F. Plebanski +5
Computer Science · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Noncommutative and Quantum Gravity Theories #Quantum Information and Cryptography #hep-th #math-ph #math.MP #math.QA #quant-ph
paper · pdf · doi:10.1088/0305-4470/35/19/311
published as J.Phys.A35:4301-4320,2002 · 27+1 pages, harvmac file, no figures
arxiv created 2001/12/07 · openalex publication_date 2002/05/03 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Second quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schrödinger spinless field is considered. Under the assumption that the phase space of the Schrödinger field is ∞ , 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 P ∞ endowed with the Fubini-Study Kählerian 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/ℏ.