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I've never heard of anyone who became an expert in Quantum Field Theory in a couple of years without having a background in Physics

An anecdote, FWIW ;)

Once Pierre Deligne, and few fellow mathematicians, annoyed at their utter lack of understanding of QFT and involved physics, decided to sit down for a year and learn some. Notes they've took during that year of effort are now a standard reference (http://www.amazon.com/Quantum-Fields-Strings-Course-Mathemat...)

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