PT Journal
AU Fioresi, R
   Lledo, MA
TI Quantum Supertwistors
SO Symmetry-Basel
JI Symmetry-Basel
PY 2021
BP 1241
EP 16pp
VL 13
IS 7
DI 10.3390/sym13071241
LA English
DE star products; superspace; non-commutative spacetime; quantum groups; quantum supergroups
AB In this paper, we give an explicit expression for a star product on the super-Minkowski space written in the supertwistor formalism. The big cell of the super-Grassmannian Gr(2|0,4|1) is identified with the chiral, super-Minkowski space. The super-Grassmannian is a homogeneous space under the action of the complexification SL(4|1) of SU(2,2|1), the superconformal group in dimension 4, signature (1,3), and supersymmetry N=1. The quantization is done by substituting the groups and homogeneous spaces by their quantum deformed counterparts. The calculations are done in Manin's formalism. When we restrict to the big cell, we can explicitly compute an expression for the super-star product in the Minkowski superspace associated to this deformation and the choice of a certain basis of monomials.
ER