Combining my reply to both your messages into one. Your article looks very interesting, I haven’t ever viewed the first quantised harmonic oscillator in that way. So I guess the propagator is just a mathematical tool to get final amplitudes. As for the Green’s function being mathematically...
Yes I think you’re right. Perhaps the answer is that the inverse of the differential operator is a term that ‘contributes’ the vacuum to vacuum amplitude, and isn’t strictly speaking an amplitude itself. After all it is describing virtual particles.
Okay thanks that makes sense. I guess my question would come down to the specific interpretation then of the differential operator in this context. Given that the inverse of the differential operator is interpreted as quantum, I guess it would make sense to interpret the differential operator...
Thanks for that. So my understanding is the original formulation has the quantum canonical momenta with the corresponding Hamiltonian, but we can get it in the form of a classical Lagrangian. Is this Lagrangain actually interpreted classically though ? I mean I know it’s equivalent to the...
Using free scalar field for simplicity.
Hi all, I have a question which is pretty simple, we have the path integral in QFT in the presence of a source term:
$$
Z[J] = \int \mathcal{D}\phi \, e^{i \int d^4x \left( \frac{1}{2} \phi(x) A \phi(x) + J(x) \phi(x) \right)}
$$
So far so good. Now...