We have systematically studied a finite-dimensional version of Feynman perturbation series with arbitrary matrices for propagators and arbitrary tensors for interaction couplings. In this formalism we obtain many old results in an elegant new manner, and we obtain a completely new fundamental integral representation for the Green's functions of boson field theories which rigorously defines these functions in our finite-dimensional version and which we hope will enable us to calculate the Green's functions in the physically important infinite-dimensional case.
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David Kershaw (1974) studied this question.
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