Noncommutative spaces and superspaces from Snyder and Yang type models

Abstract

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