2010/01/01 by L. Román Juárez, Marcos Rosenbaum
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Group (periodic table) #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Product (mathematics) #Quantization (signal processing) #Quantum #Quantum Mechanics and Applications #Scheme (mathematics) #math-ph #math.MP #msc:81Q99 #msc:81R60 #msc:81S30 #quant-ph
paper · pdf · doi:10.4303/jpm/p100803
published as J.Phys.Math. 2 (2010) 15-37 · 22 pages
openalex publication_date 2010/01/01 · arxiv created 2014/03/05 · arxiv updated 2014/03/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We investigate the Weyl-Wigner-Groenewold-Moyal, the Stratonovich, and the\nBerezin group quantization schemes for the space-space noncommutative\nHeisenberg-Weyl group. We show that the *-product for the deformed algebra of\nWeyl functions for the first scheme is different than that for the other two,\neven though their respective quantum mechanics' are equivalent as far as\nexpectation values are concerned, provided that some additional criteria are\nimposed on the implementation of this process. We also show that it is the\n*-product associated with the Stratonovich and the Berezin formalisms that\ncorrectly gives the Weyl symbol of a product of operators in terms of the\ndeformed product of their corresponding Weyl symbols. To conclude, we derive the\nstronger *-valued equations for the 3 quantization schemes considered and\ndiscuss the criteria that are also needed for them to exist.