Spinorial Snyder and Yang Models From Superalgebras And Noncommutative Quantum Superspaces

TL;DR

This paper extends Snyder and Yang quantum space-time models to superalgebras, creating supersymmetric quantum spaces and phase spaces, and compares different approaches to deriving quantum super spaces.

Contribution

It introduces superalgebra-based constructions of quantum Lorentz-covariant superspaces and phase superspaces, advancing the algebraic framework of quantum supersymmetry.

Findings

Constructed SUSY Snyder models using superalgebras.

Proposed SUSY Yang models for quantum phase superspaces.

Compared various methods of deriving quantum super spaces.

Abstract

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.