All Questions
Tagged with quantum-field-theory homework-and-exercises
188
questions with no upvoted or accepted answers
63
votes
0
answers
4k
views
How to apply the Faddeev-Popov method to a simple integral
Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
- 1,210
8
votes
1
answer
1k
views
Schrodinger Wave Functional (quantum fields) - Solving Functional Gaussian Integrals
Okay, So i'm doing some research that involves the Schrodinger representation in quantum field theory. The ground state wave functional for the Klein Gordon field is a generalized gaussian in position ...
- 305
7
votes
0
answers
369
views
LSZ Reduction Formula and Wavepackets in Peskin
In Section 7.2 of Peskin and Schroeder, the LSZ Reduction formula is discussed. I can follow the discussion leading up to the equation after (7.41) [at the bottom of Pg. 225]:
$$\sum_\lambda \int\frac{...
- 996
6
votes
0
answers
99
views
Fourier transform of Feynman Integral
In Nastase, Introduction to AdS/CFT, the first chapter talks a little about the star-triangle duality. In fact, it was claimed that the Fourier Transform of a Feynman-like diagram in position space in ...
- 980
6
votes
0
answers
988
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How can I see where this formula for a general vertex factor comes from?
I have been reading Srednicki from the beginning and doing all the exercises, and I hit a big roadblock at Q10.4, as I can't seem to figure out what Srednicki is doing in his solution. Luckily, I ...
- 161
5
votes
0
answers
188
views
Importance of an extra total derivative term in Liouville theory
In this paper on boundary Liouville theory, the authors have introduced an extra term, $-\partial_{\sigma}^2\phi$, (the last term in the equation below) in defining the stress tensor of the Liouville ...
- 544
5
votes
0
answers
538
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Feynman rules for this perturbative expansion in Grassmann variables
I'm given the integral $$ Z[w] = \frac{1}{ (2 \pi)^{n/2}} \int d^n x \prod_{i=1}^n d \overline{\theta}_i d \theta_i \exp \left( - \overline{\theta}_i \partial_j w_i (x) \theta_j - \frac{1}{2} w_i(x) ...
- 701
5
votes
0
answers
2k
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Two-point function of a free massless scalar field in Euclidean space-time
Let $\phi(x)$ be a free massless scalar field on $d$-dimesnional space-time with Euclidean metric. I am interested in the operator formalism, i.e. $\phi(x)$ is an operator satisfying $\Delta \phi=0$ ...
- 2,226
4
votes
0
answers
188
views
Feynman Rules from Generating Functional
For the following Lagrangian:
$$\mathcal{L}= \overline \psi \left(i \gamma^{\mu}D_{\mu} - m \right)\psi -\frac{1}{2}\left(F_{\mu\nu}\right)^2,$$
I'm trying to find the Feynman rules. I know that the ...
- 1,213
4
votes
0
answers
144
views
Expansion of the $S$-operator and Normal Ordering
To phrase my question I will use the example, which we used as an exercise in my introducory QFT lecture. We considered a theory of a real scalar field $\Phi$ and a complex scalar field $\phi$. The ...
- 2,196
4
votes
0
answers
486
views
Symmetry factors for feynman diagrams from complex scalar interaction term
My question regards a quantum field theory with an interaction term $${\mathcal{L_{int}}=-\frac{\lambda}{4}\phi^\dagger}^2 \phi^2.$$ It's claimed in the solutions to a problem sheet that the one-loop ...
- 167
4
votes
0
answers
656
views
Verify Furry theorem in scalar QED
I want to verify Furry theorem in scalar QED. Consider a process with N photons. Is it correct to say that at 1 loop the two classes of Feynman diagram that contribute are the following?
with $n+2m = ...
- 299
4
votes
0
answers
153
views
Solving scalar quantum field in 1+1D Milne space
So our line element is
\begin{equation}
ds^2=dt^2-a^2t^2dx^2
\end{equation}
doing following coordinate transformation
\begin{equation}
y^0=t\hspace{2pt}\cosh ax, \hspace{2pt}y^1=t\hspace{2pt}\sinh ...
- 3,043
4
votes
0
answers
413
views
Deriving a Massive Propagator from a Massless Propagator
I'm trying compute something I already know the answer to in order to test myself and gain confidence in my QFT computational skills, but I'm not getting the right factors. The text I'm following and ...
- 612
4
votes
0
answers
203
views
Vacuum expectation value for 2 point fermionic field
I was trying to compute $\langle 0|T(\psi_\alpha(x)\bar\psi_\beta(y))|0 \rangle$, i.e., the 2-point function for the Dirac field. While, I could easily compute, $\langle 0|\psi_\alpha(x)\bar\psi_\beta(...
- 592