Minimal Scales from an Extended Hilbert Space

Understand

We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations.

• As a consequence, a minimal length and a minimal mass scale are implemented.
• Our commutators do not depend on positions and momenta and we provide an extension of the coordinate coherent state approach to Noncommutative Geometry.
• We explore, as toy model, the corresponding quantum field theory in a (2+1)-dimensional spacetime.