Twist-Related Geometries on q-Minkowski Space

The role of the quantum universal enveloping algebras of symmetries in constructing the noncommutative geometry of the space–time including vector bundles, measure, equations of motion and their solutions is discussed. In the framework of the twist theory, the Klein–Gordon–Fock and Dirac equations on the quantum Minkowski space are studied from this point of view for the simplest quantum deformation of the Lorentz algebra induced by its Cartan subalgebra twist.