Global space-time symmetries of quantized Euclidean and Minkowski superspaces

Abstract

Abstract Starting with assumptions both simple and natural from “physical” point of view we present a direct construction of the 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 = \frac{1}{2} $ supersymmetry as well as its three parameter extension. The resulting symmetry transformations — supersymmetric extension of θ — Euclidean group can be regarded as global counterpart of appropriately twisted Euclidean superalgebra that has been shown to preserve $ N = \frac{1}{2} $ supersymmetry.