Abstract
The author considers an Abelian gauge field theory on Euclidean partially compactified spacetime TN*Rn for arbitrary N and n. The one-loop effective potential generated by quantum fluctuations of a massive scalar field, minimally coupled to a constant background Abelian gauge potential is calculated for arbitrary compactification lengths L1,. . .,LN of the multi-dimensional torus. In particular the topologically generated mass of the gauge field is obtained and its complicated dependence on the parameters involved (compactification lengths, mass M of the scalar field) is given explicitly. It is found that the topologically generated mass is positive for arbitrary N and n and that it does not depend on a renormalization parameter. For n>2 the limit M to 0 is smooth, but for n=0,1,2 zero modes play a crucial role and the generation of real or imaginary gauge field masses is possible.
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