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Mathematics of the Feynman path integral Vassili N. Kolokoltsov - IMA

of the function exp{iS}, where S is the classical action along the paths. It seems that. rigorously the corresponding measure was not constructed even for the case .

http://www.ima.umn.edu/prob-pde/reprints-preprints/kolokoltsov/serbia.ps

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Functional integrals, Wightman functions, and rigorous QFT

For rigorous quantum field theory one essentially avoids the path integral, because it is difficult to give it a rigorous meaning when the action is not quadratic.

http://www.mat.univie.ac.at/~neum/physfaq/topics/functionalW