Linked Questions

2 votes
0 answers

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 ...
akreuzkamp's user avatar
1 vote
0 answers

Why are tree-level diagrams classical? [duplicate]

I see this statement from time to time. But when I look at scattering in QED or phi-4 theory, I don't understand how classical calculation can reproduce these amplitudes. To what extent is this ...
Bababeluma's user avatar
54 votes
6 answers

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 ...
user avatar
29 votes
3 answers

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 $$\phi_c(x)\equiv\langle 0|\hat{\phi}(x)|0\rangle_J$$ ...
SRS's user avatar
  • 26.6k
18 votes
2 answers

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 ...
drandran12's user avatar
19 votes
3 answers

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)}...
dixi's user avatar
  • 321
11 votes
2 answers

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 ...
Ogawa Chen's user avatar
  • 1,171
13 votes
2 answers

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 ...
KF Gauss's user avatar
  • 7,882
7 votes
3 answers

How can the mass of an unstable composite particle become complex?

To show where the resonances in cross sections come from, one usually considers the exact propagator in the interacting theory, which for a scalar is $$iG(p^2)=\frac{i}{p^2-m_R^2+\Sigma(p^2)+i\epsilon}...
F.Burton's user avatar
  • 153
9 votes
2 answers

Showing that loop corrections are quantum effects in Quantum Field Theory

Say I have a theory in four dimensions with the Lagrangian density \begin{equation} \mathcal{L} = \frac{1}{2} \partial_\mu \phi \partial^\mu\phi - \frac{1}{2} m^2 \phi^2. \end{equation} This has the ...
QFTheorist's user avatar
8 votes
2 answers

The Schrödinger equation as an Euler-Lagrange equation

In section 1.2 on p. 14 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\...
SRS's user avatar
  • 26.6k
6 votes
1 answer

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?
mandylel's user avatar
4 votes
2 answers

Interpreting generating functional as sum of all diagrams

The generating functional is defined as: $$Z[J] = \int \mathcal{D}[\phi] \exp\Big[\frac{i}{\hbar}\int d^4x [\mathcal{L} + J(x)\phi(x)]\Big].$$ I know this object is used as a tool to generate ...
CBBAM's user avatar
  • 3,340
2 votes
2 answers

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 ...
mathripper's user avatar
2 votes
2 answers

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 ...
B.Hueber's user avatar
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