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1. ### Instanton contribution to two point function

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...
2. ### Symmetry, Lagrangian, Qm, and diff eqs.

I am not sure if I understood your question exactly and my reply may sound trivial. Anyway, when you have a symmetry there are invariants associated with each of those symmetries (Noether's Theorem). In other words some quantities will be conserved during, let's say, a collision experiment like...
3. ### Effective action from the background field

Hello, Assuming that I have a pure U(1) gauge theory. The partition function can be written as Z=\int D(A) \exp (-F_{\mu\nu} F^{\mu\nu}) If I want to find the effective action in terms of an external classical field I can write it in terms of A\rightarrow A+B where B is background and then...
4. ### Connection between Free Energy and Action

Could anyone please, explain the connection between the Free Energy and the Action? I know the definitions of each but not sure about the connection. I read somewhere that the free energy is the same as the action when calculated "on-shell". What does this "on-shell" thing mean in this...
5. ### Integration in path integral formalism?

Hi, Does anyone know how this integral is calculated \int[dx] x_i x_j \exp \{ - (\frac{1}{2} \sum_{rs} A_{rs}x_r x_s+\sum_r L_r x_r ) \} Thanks