Differential calculus on q-Minkowski space

Abstract

We wish to report here on a recent approach to the non-commutative calculus on $q$-Minkowski space which is based on the reflection equations with no spectral parameter. These are considered as the expression of the invariance (under the coaction of the $q$-Lorentz group) of the commutation properties which define the different $q$-Minkowski algebras. This approach also allows us to discuss the possible ambiguities in the definition of $q$-Minkowski space ${\mathcal{M}}_q$ and its differential calculus. The commutation relations among the generators of ${\mathcal{M}}_q$ (coordinates), ${\mathcal{D}}_q$ (derivatives), ${\Lambda }_q$ (one-forms) and a few invariant (scalar) operators are established and compared with earlier results.