Feynman path integrals in a phase space

1980/11/30 by F A Berezin, F. A. Berezin · 13 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies

paper · doi:10.1070/pu1980v023n11abeh005062

openalex publication_date 1980/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Feynman path integrals in a phase space are analyzed in detail. The analysis is based on the theory of operator symbols, in contrast with the traditional approach based on the direct use of canonical commutation relations. Particular attention is paid to the Weyl and Wick symbols, which are the most important in applications. The set of paths on which the integral is concentrated is studied. It is found that these paths are always discontinuous. This discontinuity is responsible for errors in certain papers on path integrals in a phase space. The most important properties of the Weyl and Wick symbols are reviewed.

Cited by

• Quantization and Algebraic Index
• High-energy photon hologram of a photon gas
• Emergent Quantumness in Neural Networks
• Discrete dynamics and supergeometry
• Fluctuations as stochastic deformation
• Quantum thermodynamics of systems with anomalous dissipative coupling
• Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems
• Two-dimensional quantum Heisenberg antiferromagnet: Effective-Hamiltonian approach to the thermodynamics
• Generating all Wigner functions
• Symplectic Dirac–Kähler fields
• Effective descriptions of complex quantum systems: path integrals and operator ordering problems
• A path integral approach to noncommutative superspace
• Thermodynamics of quantum dissipative many-body systems

Related

• An Introduction into the Feynman Path Integral
• On Hilbert's sixth problem
• Classification of Solvable Feynman Path Integrals
• Complex Path Integrals and the Space of Theories
• The Feynman integral path a Henstock integral: a survey and open problems