Hey guys, I have a doubt. I was wondering if it is possible to have a generating function Z[J] where its integral has not a linear dependence on J(t), but a quadratic or even cubic dependence, like Z[J]=∫Dq exp{S[q] + ∫ J²(t) q(t)dt}, and how this would alter the calculation of the n-point functions. Thaks!
It's not reasonable b/c you introduce the source J only to construct the n-point functions for vanishing source J=0; with a J² term after setting J=0 all q-depenedent terms would vanish