Work

Phase space representation of the density operator: Bopp pseudodifferential calculus and Moyal product

Year: 2025

Type: article

Abstract: Bopp shifts, introduced in 1956, played a pivotal role in the statistical interpretation of quantum mechanics. As demonstrated in our previous work, Bopp’s construction provides a phase-space perspective of quantum mechanics that is closely connected to the Moyal star product and its role in deformation quantization. In this paper, we both review and expand on our exploration of Bopp quantization, emphasizing its relationship with the Moyal product and its applications in elementary deformation quantization. Notably, we apply these constructions to the density operator, which represents mixed states in quantum mechanics, offering novel insights into its role within this framework.

Source: Journal of Pseudo-Differential Operators and Applications

DOI: 10.1007/s11868-024-00674-3

Author: Maurice de Gosson

Institutions: University of Vienna, Austrian Academy of Sciences, Acoustics Research Institute

Language: English

Topic: Quantum Mechanics and Applications

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Österreichischen Akademie der Wissenschaften, Austrian Science Fund