Generalized Weyl Quantization and Time

• Main Authors: Romeo, Daisy A, Nable, Job A
• Format: text
• Published: Archīum Ateneo 2021
• Subjects: Weyl Quantization; time; phase space quantum mechanics; operator ordering; Geometry and Topology; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/152; https://projecteuclid.org/proceedings/geometry-integrability-and-quantization/Proceedings-of-the-Twenty-Second-International-Conference-on-Geometry-Integrability/Chapter/Generalized-Weyl-Quantization-and-Time/10.7546/giq-22-2021-242-252?tab=ChapterArticleLink
• Institution: Ateneo De Manila University

This work presents quantization of time of arrival functions using generalized Stratonovich-Weyl quantization. We take into account the ordering problems involved, mainly the Born-Jordan and the symmetric ordering schemes. We call attention to the combination of the group theoretic methods usually employed in Weyl quantization with the implementation of different ordering schemes via integral kernel factors. It is possible to, and we do, apply the Pegg-Barnett method to the quantization of time to address physical issues such as boundedness and self-adjointness.