The Measure from Schwinger-Dyson Equations

dt Jq) . (2) The ~ → 0 limit of Z[J ] is dominated by configurations near to the solutions of δS δq +J = 0. On the other hand, ~ → 0 corresponds to classical physics given by δI δq + J = 0, where I is the action. From this we see that S[q] = I[q] + ~ i M [q] . (3) M [q] is the measure term. This is as far as the usual functional formalism takes us — namely, there is no way to determine the measure term. The only way to do this has It is common to write the integrand of (2) in terms of the action. The path integral measure is then dμ = [dq] expM [q]. Lack of knowledge about M translates into lack of knowledge about dμ.