Noncommutative spaces and superspaces from Snyder and Yang type models

Abstract

The relativistic 𝐷 = 4 Snyder model is formulatedin terms of 𝐷 = 4 𝑑𝑆 algebra 𝑜 ( 4 , 1 ) generators, with noncommutative Lorentz-invariant Snyder quantum space-time provided by 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 𝑂 ( 5 , 1 ) 𝑂 ( 3 , 1 ) or 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).