文档介绍：arXiv:gr-qc/9906059 v2 25 Jul 1999
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1 Introduction
To control the divergences which from the very beginning had plagued quan-
tum electrodynamics, Heisenberg already in the 1930’s proposed to replace
the space-time continuum by a lattice structure. A lattice however breaks
Lorentz invariance and can hardly be considered as fundamental. It was Sny-
der [201, 202] who first had the idea of using a mutative structure at
small length scales to introduce an effective cut-off in field theory similar to a
lattice but at the same time maintaining Lorentz invariance. His suggestion
came however just at the time when the renormalization program finally suc-
cessfully became an effective if rather ad hoc prescription for predicting numbers
from the theory of quantum electrodynamics and it was for the most part ig-
nored. Some time later von Neumann introduced the term ‘mutative
geometry’ to refer in general to a geometry in which an algebra o