Generalized Weyl transform for operator ordering: Polynomial functions in phase space

DOI10.1063/1.4907561zbMath1311.81212OpenAlexW2080609742MaRDI QIDQ5178189

Herbert B. Domingo, Eric A. Galapon

Publication date: 13 March 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4907561

Mathematics Subject Classification ID

Quantization in field theory; cohomological methods (81T70) Geometry and quantization, symplectic methods (81S10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items

On the invertibility of Born-Jordan quantization, Euler polynomials and identities for non-commutative operators, Generalized Born-Jordan distributions and applications, Born-Jordan pseudodifferential operators with symbols in the Shubin classes, Generalized Weyl quantization and time, From Weyl to Born-Jordan quantization: the Schrödinger representation revisited, Bypassing the Groenewold–van Hove obstruction on ${{\mathbb{R}}}^{2n}$: a new argument in favor of Born–Jordan quantization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Preferred quantization rules: Born-Jordan versus Weyl. The pseudo-differential point of view
• Generalized functions. Theory and technique
• The algebra of Weyl symmetrised polynomials and its quantum extension
• Some examples and applications of Fedosov's star products and deformation quantization
• Derivations of Lie brackets and canonical quantisation
• General ordering problem and its combinatorial roots
• Quantum first time-of-arrival operators
• On the Groenewold–Van Hove problem for R2n
• The Bender-Dunne basis operators as Hilbert space operators
• General Space-Momentum Commutation Relation
• On the principles of elementary quantum mechanics