Quantum groups and quantum field theory with nonzero minimal uncertainties in positions and momenta

Abstract

Various regularisation techniques are presently emerging from the field of noncommutative geometry. We focus on the possibility of introducing nonzero minimal uncertainties in positions and momenta into the quantum field theoretical framework. Thereby we use techniques that have been developed in the field of quantum groups. The regularisation of a quadratic ultraviolet divergency inφ 4 theory is given explicitely. We also discuss the underlying idea that such uncertainties in position or momentum measurements originate in gravity.