Minimal Length Uncertainty Relation and Ultraviolet Regularisation

Abstract

Studies in string theory and quantum gravity suggest the existence of a finite lower limit $Δx_0$ to the possible resolution of distances, at the latest on the scale of the Planck length of $10^{-35}m$. Within the framework of the euclidean path integral we explicitly show ultraviolet regularisation in field theory through this short distance structure. Both rotation and translation invariance can be preserved. An example geometry is studied in detail.