Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 049, 10 pages      arXiv:2403.05464      https://doi.org/10.3842/SIGMA.2024.049

Generalized Yang Poisson Models on Canonical Phase Space

Tea Martinić Bilać a, Stjepan Meljanac b and Salvatore Mignemi cd
a) Faculty of Science, University of Split, Rudera Boškovića 33, 21000 Split, Croatia
b) Division of Theoretical Physics, Ruder Bošković Institute, Bijenička cesta 54, 10002 Zagreb, Croatia
c) Dipartimento di Matematica, Università di Cagliari, via Ospedale 72, 09124 Cagliari, Italy
d) INFN, Sezione di Cagliari Cittadella Universitaria, 09042 Monserrato, Italy

Received March 12, 2024, in final form May 29, 2024; Published online June 10, 2024

Abstract
We discuss the generalized Yang Poisson models. We construct generalizations of the Yang Poisson algebra related to $\mathfrak{o}(1,5)$ algebra discussed by Meljanac and Mignemi (2023). The exact realizations of this generalized algebra on canonical phase space are presented and the corresponding differential equations are solved in simple cases. Furthermore, we discuss the Poisson algebras related to $\mathfrak{o}(3,3)$ and $\mathfrak{o}(2,4)$ algebras.

Key words: Yang Poisson model; generalized Yang Poisson model; realizations.

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