  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.
