Noncommutative spaces and superspaces from Snyder and Yang type models

Abstract

The relativistic $D=4$ Snyder model is formulated in terms of $D=4$ $dS$ algebra $o(4,1)$ generators, with noncommutative Lorentz-invariant Snyder quantum space-time provided by $\frac{O(4,1)}{O(3,1)}$ coset generators. Analogously, in relativistic $D=4$ Yang models the quantum-deformed relativistic phase space is described by the algebras of coset generators $\frac{O(5,1)}{O(3,1)}$ or $\frac{O(4,2)}{O(3,1)}$. We extend these algebraic considerations by using respective $dS$ superalgebras, which provide Lorentz-covariant quantum superspaces (SUSY Snyder model) as well as relativistic quantum phase super spaces (SUSY Yang model).

20 pages, CORFU 2021 conference paper. arXiv admin note: text overlap with arXiv:2110.13697

Cited by in corpus (1)

• $\hslash$-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking