Instanton contribution to two point function

[physengineer]

Hello,

I would appreciate it if anyone could help me with this problem: can there be any instantonic contribution to the following generic two-points function?

$$\left \langle \varphi(x) \varphi(y) \right\rangle= \int D\varphi D A \varphi(x) \varphi(y) \exp \left( -S_E [\varphi,A] \right),$$
where $S_E$ is an Euclidean action, $\varphi$ bosonic field and $A$ is the gauge field.

I am not sure even if my question makes any sense. I have seen people calculate instability of the vacuum of the action $S_E$, which was just from the partition function. I do not know if I have to be careful about instantons when I calculate a two-points function or not.

Thank you in advance!

 

[azntoon]

Yes, there can be an instantonic contribution to the two-point function. In general, instantons are solutions to the classical equations of motion that have finite action and represent tunneling between different vacua. In the context of the two-point function, there can be instantonic contributions that arise from the path integral over all possible configurations of the fields. These contributions can be calculated using the semiclassical approximation, by treating the instanton as a saddle point in the action and expanding around it. This can result in an extra contribution to the two-point function, depending on the specific form of the action.