Noncommutative geometric regularization

Studies in string theory and in quantum gravity suggest the existence of a finite lower bound to the possible resolution of lengths which, quantum theoretically, takes the form of a minimal uncertainty in positions Δx₀. A finite minimal uncertainty in momenta Δp₀ has been motivated from the absence of plane waves on generic curved spaces. Both effects can be described as small noncommutative geometric features of space-time. In a path integral approach to the formulation of field theories on noncommutative geometries, we can now generally prove IR regularization for the case of noncommutative geometries which imply minimal uncertainties Δp₀ in momenta.