Path Integral is Simpler and Hotter

In almost all graduate courses of quantum field theory, it seems it is always a norm that the lecturer teaches the approach of canonical quantization first. They would leave path integrals to the end, or simply omit it, because of the notion that path integrals are way too advanced to beginners.

But it is not my belief. I think the approach of path integrals, calculational-wise, is much simpler! Because in functional integrals, the normal ordering of the operators have already been considered. The operators are naturally written in terms of the coherent states, you do not have those extra terms in the Wick’s theorem. Besides, the propagators can be evaluated in a much more easy and direct way using the generating functional. Moreover, in path integrals, there are fewer commutation relations that you have to worry about, avoiding a lot of unnecessary careless mistakes. Carrying out the calculation of the path integrals is just neat.

The approach of path integrals provide a clearer physical picture of what is going on. The relationship of the quantum field theory and the classical physics is more obvious in path integrals: the exponent of the path integrals can be well approximated by the action of the classical path (, and it is exact if the integrand is Gaussian.) Path integrals can be easily related to probability distribution, while the quantum theory is itself probabilistic.

Given the above reasons, I believe that the teachers of the quantum field theory should be more open to the options of teaching path integrals in the first place.

Reference: A. Zee, Quantum Field Theory in a Nutshell; R. P. Feynman, QED: the Strange Theory of Light and Matter; R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals

http://www.facebook.com/group.php?gid=29472939420