Abstract
A generalization of gauge theories based on non-Abelian matrix groups to the operator group of translations is given. It leads to the concept of local translation invariance and to the existence of an operator-valued gauge field in Minkowski space. Its dynamics is uniquely determined using the RG and new heat kernel techniques developed in an appendix. The resulting theory is shown to be a gauge theory of gravitation which is physically complementary and mathematically equivalent to the general theory of relativity.
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