All Questions
109 questions
5votes
1answer
245views
How to understand basics of propagators and Wightman function?
Professor David Tong, in QFT notes 2 at section 2.7 above eq. (2.90) writes: "Prepare a particle at spacetime point $y$. What is the amplitude to find it at point $x$? We can calculate this: $ \...
6votes
1answer
116views
Expansion of $(S_{I}[\bar{\alpha},\alpha])^n$ in the proof of the linked-cluster theorem
On P.192 of Piers Coleman's "Introduction to many body physics", he uses Sam Edwards' replica trick to show that Green's function $$G(1-2)=\sum{\text{two-leg linked-cluster diagram}}\tag{7....
2votes
2answers
166views
Charge renormalization and wavefunction renormalization in QED
In QED, we usually say that charge renormalization is a consequence of vacuum polarization, because of the virtual electron-position pairs, the bare charge is shielded. It is intuitively ...
- 453
0votes
1answer
78views
How are path integral functional derivatives taken when a single field couples to two independent sources?
I was reading a paper https://arxiv.org/abs/2005.01515 equation (1.6) about dark photon mixing and came across the lagrangian \begin{equation} \mathcal{L}_{0}=gJ_{\mu}A^{\mu}+g'J'_{\mu}A^{\mu} \end{...
0votes
0answers
70views
Determine 3-point function by conformal symmetry
I already posted question to math stack but I haven't yet gotten answer. So, I ask here. I'd like to know a form of functions (called 3-point function) that have symmetry under some transformation. ...
1vote
0answers
81views
Propagators in the Klein-Gordon theory
I am currently doing QFT to be more precise the theory of the Klein-Gordon field and I'm a bit confused about the propagators. That's how I understood it: In non relativistic quantum mechanics the ...
8votes
1answer
1kviews
Photon propagator in path integral vs. operator formalism
I am self-studying the book "Quantum field theory and the standard model" by Schwartz, and I am really confused about the derivation of the Photon propagator on page 128-129. He starts ...
- 776
5votes
1answer
1kviews
Why are 2-point functions Green's functions?
I asked a question about this earlier but I think it was unfocused so I have rephrased it and asked it again. The propagator/two-point function $\langle \phi(x_1)\phi(x_2)\rangle$ for any theory can ...
- 4,500
2votes
0answers
46views
Is there any intuitive reason why 2-point functions are inverse operators to the free Lagrangian? [duplicate]
To compute $n$-point functions in quantum field theory we use Wick's theorem to reduce this problem to computing 2-point functions. In many textbooks, such as Peskin & Schroeder, the 2-point ...
- 4,500
2votes
2answers
99views
Why $n-1$ point function vanishes in $D=0$ scalar theory?
If we consider a $D=0$ theory with the Lagrangian: $$\mathcal{L}[\phi]=g\phi^n+J\phi$$ And its Green functions: $$G_n=\langle\phi^n\rangle_{J=0}=\frac{1}{Z[0]}\frac{\delta^nZ[J]}{\delta J^n}|_{J\...
- 378
3votes
1answer
164views
Amputated connected 2-point function is inverse to connected 2-point function
Let $D_n$ denote the $n$-point correlation function consisting of only connected diagrams. We may decompose this as an integral of two products. The first factor consists of a product over the $n$ ...
- 4,500
5votes
1answer
286views
How does one rigorously define two-point functions?
Let $\mathscr{H}$ be a complex Hilbert space, and $\mathcal{F}^{\pm}(\mathscr{H})$ be its associated bosonic (+) and fermionic (-) Fock spaces. Given $f \in \mathscr{H}$, we can define rigorously the ...
- 1,283
0votes
0answers
88views
Zero temperature Green function as limit of finite temperature Green function
Consider a system of $N$ fermions in a periodic box $\Lambda \subset \mathbb{R}^{d}$. The Hamiltonian of the system is: $$H_{N} = \sum_{k=1}^{N}(-\Delta_{x_{k}}-\mu) + \lambda \sum_{i< j}V(x_{i}-x_{...
- 1,283
1vote
0answers
102views
Functional derivative of a Green function
I'm trying to prove that, given the Hamiltonian $\hat{H} + \int d\mathbf{x} \hat{n}(\mathbf{x})\varphi(\mathbf{x}, t)$, where $\varphi(\mathbf{x}, t)$ is some external field and $\hat{S}$ the ...
- 173
1vote
1answer
175views
Calculation of $ \gamma(\lambda) $ in massless renormalizable scalar field theory
In Peskin & Schroeder p.413 and 414, the Callan-Symanzik equation for a 2-point Green's function is used to calculate $ \gamma(\lambda) $ for a massless renormalizable scalar field theory. The two-...
- 1,115
