Global Space-Time Symmetries of Quantized Euclidean and Minkowski Superspaces

TL;DR

This paper constructs and analyzes quantum symmetry supergroups that preserve (anti)commutation relations in Euclidean and Minkowski superspaces, extending supersymmetry transformations to deformed, non(anti)commuting parameter spaces.

Contribution

It provides a direct construction of transformations preserving superspace (anti)commutation relations and introduces quantum symmetry supergroups compatible with these deformations.

Findings

Constructed transformations act on deformed superspaces similarly to classical ones.

Identified quantum supergroups extending N=1/2 supersymmetry.

Established the relation between twisted superalgebras and quantum symmetry groups.

Abstract

Starting with assumptions both simple and natural from "physical" point of view we present a direct construction of transformations preserving wide class of (anti)commutation relations which describe Euclidean/Minkowski superspace quantizations. These generalized transformations act on deformed superspaces as the ordinary ones do on undeformed spaces but they depend on non(anti)commuting parameters satisfying some consistent (anti)commutation relations. Once the coalgebraic structure compatible with the algebraic one is introduced in the set of transformations we deal with quantum symmetry supergroup. This is the case for intensively studied so called N=1/2 supersymmetry as well as its three parameter extension. The resulting symmetry transformations - supersymmetric extension of theta-Euclidean group can be regarded as global counterpart of appropriately twisted Euclidean superalgebra that has been shown to preserve N=1/2 supersymmetry.