I'm reading Siegel's fields page 278 section IIIB3. I'm interested to know how does the transition amplitude <Ψf|Ψi> change under diffeomorphisms of the target space. We use the worldline action S=∫dτ[−1/2e−1gmn˙Xm˙Xn] for simplicity and we want to know how does ∫dXfdXi∫DXe−iSΨ∗f(Xf)Ψi(Xi)@pathintegral