Linked Questions

2
votes
0answers
67 views

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 ...
48
votes
5answers
8k views

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 ...
17
votes
2answers
2k views

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 ...
18
votes
3answers
2k views

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 $$\phi_c(x)\equiv\langle 0|\hat{\phi}(x)|0\rangle_J$$ ...
13
votes
3answers
3k views

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)}...
7
votes
2answers
3k views

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 ...
9
votes
2answers
1k views

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 ...
5
votes
2answers
2k views

The Schrödinger equation as an Euler-Lagrange equation

In the book Many-Particle Physics by Gerald D. Mahan, he points out that the Schrödinger equation in the form $$i\hbar\frac{\partial\psi}{\partial t}~=~\Big[-\frac{\hbar^2\nabla^2}{2m}+U(\textbf{r})\...
2
votes
1answer
634 views

Why coupling constants with negative mass dimensions lead to non-renormalizable theories?

can somebody explain or point to the relating mathematics showing Why coupling constants with negative mass dimensions lead to non-renormalizable theories?
2
votes
2answers
269 views

Precise definition of the vertex factor

Just a short question about the vertex factor in QFT. When I have an interaction Lagrangian $$\mathcal{L}_{\mathrm{int}}=-\frac{\lambda}{3!}\phi^3$$ with a real scalar field $\phi$, is the vertex ...
2
votes
2answers
159 views

Some details on Wilson's method of integrating out high momenta in Peskin & Schroeder p.397

When P&S explain Wilson's method of integrating out high momenta they start from the Euclidean path integral of the $\phi^4$-theory (eq. (12.3)) and then define in the following: $$\hat{\phi}(k):=...
2
votes
2answers
239 views

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 ...
5
votes
1answer
374 views

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 ...
4
votes
1answer
181 views

Loop counting for determinants and anomalies

I am trying to understand an argument for why anomalies are one-loop exact, given by Bilal in Lectures on Anomalies. The relevant paragraph is reproduced here: Let us first explain why the anomaly ...
2
votes
2answers
145 views

Symmetry factor of a loop diagram with gauge-bosons

I have learnt in the lecture that the symmetry factor of the following diagram is 1/2: where the line corresponds to a gluon. But why is this the case? We get 1/2 from 2nd order in pertubation ...

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