Spinorial Snyder and Yang models from superalgebras and noncommutative quantum superspaces

The relativistic Lorentz-covariant quantum space-times obtained by Snyder can be described by the coset generators of (anti) de-Sitter algebras. Similarly, the Lorentz-covariant quantum phase spaces introduced by Yang, which contain additionally quantum curved fourmomenta and quantum-deformed relativistic Heisenberg algebra, can be defined by suitably chosen coset generators of conformal algebras. We extend such algebraic construction to the respective superalgebras, which provide quantum Lorentz-covariant superspaces (SUSY Snyder model) and indicate also how to obtain the quantum relativistic phase superspaces (SUSY Yang model). In last Section we recall briefly other ways of deriving quantum phase (super)spaces and we compare the spinorial Snyder type models defining bosonic or fermionic quantum-deformed spinors. (C) 2021 The Authors. Published by Elsevier B.V.

Automated summary

This article discusses the relativistic Lorentz-covariant quantum space-times obtained by Snyder and the Lorentz-covariant quantum phase spaces introduced by Yang, as well as their extensions in superalgebras. The article also briefly reviews other ways of deriving quantum phase spaces and compares different types of Snyder models.