Intrinsic Regularization in a Lorentz invariant non-orthogonal Euclidean Space

Abstract

It is shown that the Lorentz transformations can be derived for a non-orthogonal Euclidean space. In this geometry one finds the same relations of special relativity as the ones known from the orthogonal Minkowski space. In order to illustrate the advantage of a non-orthogonal Euclidean metric the two-point Green's function at x = 0 for a self-interacting scalar field is calculated. In contrast to the Minkowski space the one loop mass correction derived from this function gives a convergent result due to an intrinsic regularization parameter called effective dimension. This parameter is an entropy related measure for the information loss caused by quantum fluctuations of the metric at energies higher than the Planckian limit.