Symbol Correspondence for Euclidean Systems

• Main Authors: Natividad, Laarni B, Nable, Job A
• Format: text
• Published: Archīum Ateneo 2021
• Subjects: Euclidean motion group; Moyal star-product; unitary representations; Weyl transform; Wigner function; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/192; https://projecteuclid.org/journals/journal-of-geometry-and-symmetry-in-physics/volume-62/issue-none/Symbol-Correspondence-for-Euclidean-Systems/10.7546/jgsp-62-2021-67-84.short?tab=ArticleLink
• Institution: Ateneo De Manila University

The three main objects that serve as the foundation of quantum mechanics on phase space are the Weyl transform, the Wigner distribution function, and the ⋆-product of phase space functions. In this article, the ⋆-product of functions on the Euclidean motion group of rank three, E(3), is constructed....