# What's the relation between perturbative and nonperturbative QFT?

In case of any miscommunication let me describe my understanding of the meaning of "perturbative" and "non-perturbative", and correct me if something is wrong: In a perturbatively defined QFT the fields are quantized as free fields, and the interaction is constructed by multiplying free fields operators, hereafter particles can scatter with each other; non-perturbatively defined QFT is any QFT in which the interaction is not constructed by the above-described method, e.g. a lattice QFT.

Now I'm curious about the connection between two constructions. The possibilities I can imagine are the following:

1. Perturbative and non-perturbative QFT are complementary to each other, they are both approximations of some underlying theory.There are things perturbative QFT can cover which non-perturbative QFT can't, and vice versa.

2. Perturbative QFT is contained in non-perturbative QFT, thus can be derived from it as some kind of limiting situation, however some calculations are more efficient in perturbative QFT.

Which one is correct? My sanity favors (1), but "non-perturbative" really sounds like a more powerful word to me so I can't help thinking (2) is possible. I'd really appreciate a comprehensive explanation on the issue.

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Related: physics.stackexchange.com/q/31930/2451 and links therein. –  Qmechanic Jul 31 '12 at 8:42