We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure.

The Bethe-Salpeter equation in non-commutative QED (NCQED) is considered for three-body bound state. We study the non-relativistic limit of this equation in the instantaneous approximation and derive the corresponding Schrödinger equation in non-commutative space. It is shown that the experimental data for Helium atom puts an upper bound on the magnitude of the parameter of non-commutativity, θ...

We review a procedure of factorizing the Minkowski space Dirac operator over a~suitable superspace, discuss its Euclidean version and apply worked out formalism in case od an almost-commutative operator. The presented framework is attempt to reconcile non-commutative geometry supersymmetry.