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I would like to know if there has been any progress recently toward giving the Feynman integral a rigorous definition. I heard that Richard Borcherds is working on giving quantum field theory a rigorous foundation, but I am not familiar with his work. Perhaps someone here on the M.S.E. who is familiar with what he does can give some insight?

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    This was asked on mathoverflow: http://mathoverflow.net/questions/24823/the-mathematical-theory-of-feynman-integrals2016-10-17

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