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...)
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...)