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### Nonlinear superposition and self-interaction in classical field theory [duplicate]

I am learning QFT (in a path integral formalism) and one thing I'm struggling with is that self-interaction is supposed to be a quantum phenomenon, not apparent in classical non-linear field theory. I ...
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### Tree level QFT and classical fields/particles

It is well known that scattering cross-sections computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scattering ...
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### How do non-linear equations lead to self-interaction?

In my life I hear/read this statement a lot: A non-linear equation or theory leads to self-interactions. For example in GR, we say that gravity can interact with itself because it is non-linear. For ...
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### In what sense is the proper/effective action $\Gamma[\phi_c]$ a quantum-corrected classical action $S[\phi]$?

There is a difference between the classical field $\phi(x)$ (which appears in the classical action $S[\phi]$) and the quantity $\phi_c$ defined as $$\phi_c(x)\equiv\langle 0|\hat{\phi}(x)|0\rangle_J$$ ...
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### Proof that the effective/proper action is the generating functional of one-particle-irreducible (1PI) correlation functions

In all text book and lecture notes that I have found, they write down the general statement \begin{equation} \frac{\delta^n\Gamma[\phi_{\rm cl}]}{\delta\phi_{\rm cl}(x_1)\ldots\delta\phi_{\rm cl}(x_n)}...
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### Intuition behind Linked Cluster Theorem: connected vs. non-connected diagrams

Within statistical physics and quantum field theory, the linked cluster theorem is widely used to simplify things in the calculation of the partition function among other things. My question has the ...
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### How to understand the idea of functional renormalization group?

I have been looking at how to use the functional RG method in many-body systems, but I don't quite get the idea of it, it looks different from Wilson's RG approach (eg. why shall we integrate out the ...
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### Feynman diagram for double-bubble vacuum graph in $\phi^4$ theory

I was trying to do an exercise from the book "QFT for the Gifted Amateur" by Tom Lancaster. It involves computing the momentum space amplitudes of some Feynman diagrams. I was trying to ...
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### Combinatorics geometric series two-point function

In this answer Proof of geometric series two-point function it is said: Now what about the coefficients in front of each Feynman diagram? Due to the combinatorics/factorization involved it ...