I understood that quantum field theory is essentially based on a problematic mathematical basis. Can someone please explain what is the fundamental problem to formulate QFT as a rigorous mathematical theory? It's clear that it has to do with renormalization but similar techniques are already exist in analytically number theory (and are considered to be a mathematical theory).
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2Be aware that there are multiple QFT's, some of which aren't so problematic; see Which QFTs were rigorously constructed?. – Nov 15 '13 at 01:00
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Related: http://physics.stackexchange.com/q/27665/2451 and links therein. – Qmechanic Nov 15 '13 at 02:16