All Questions
48
questions
0
votes
2
answers
63
views
Are loops counted twice in Feynman diagrams?
Consider the 2 point function in $\phi^4$ theory which is given as something proportional to
$$\int D(x-z) D(y-z) D(z-z) d^4 z,$$
where $D$ is the propagator. The corresponding Feynman diagram looks ...
- 3,350
4
votes
2
answers
131
views
Miraculous cancellations in a-priori non-renormalizable theories
Einstein's gravity is non-renormalizable since its coupling constant in 4D (I would like to limit the discussion to 4D) has negative mass dimension of -2.
Nevertheles it has been hoped that -- may be ...
- 9,778
2
votes
1
answer
198
views
Symmetry Factor and Wicks Theorem
I have a problem with a particular kind of exercise. The question is:
Consider $\phi^4$-theory with $\mathcal{L}_\text{int}=-\frac{\lambda}{4!}\phi^4$. Give the symmetry factors of the diagram and ...
- 23
4
votes
2
answers
510
views
Please help me to understand calculation of the symmetry factor of Feynman diagrams (Lancaster & Blundell's Quantum field theory)
I am reading the Lancaster & Blundell's Quantum field theory for the gifted amateur, p.183, Example 19.5 (Example of symmetry factors of several Feynman diagrams) and stuck at understanding ...
- 323
0
votes
1
answer
163
views
Vertex in Feynman diagram
The Taylor expansion for $e^x$ to 2nd order is
$$e^x = 1 + x + x^2/2$$
If we look at the unitary operator for the $\phi^4$ theory
$$\exp\left[-i\frac{\lambda}{4!}\int{\phi^4}dt\right] , $$
we can also ...
user310742
1
vote
1
answer
55
views
"Mirrored" diagrams of $n$-point functions
Suppose we are calculating the two-point function $\langle\phi(x_1)\phi(x_2) \rangle$ and we've obtained a loop diagram of the kind on the left. Will there necessarily also be a diagram as on the ...
- 298
1
vote
0
answers
83
views
Finding symmetry factors
Suppose we have a two-loop graph that looks like two balloons next to each other or stacked on top of each other. What are the symmetry factors of these graphs?
Note that I'm trying to compute a two-...
- 298
1
vote
1
answer
105
views
Where the $1/2!$ term comes from in the symmetry factor for Feynman diagram?
I'm trying to understand the symmetry factor for this diagram:
The combinatorial factors make sense to me, and the two vertices in $\phi^4$ theory give two $1/4!$ terms. I wonder how the $1/2!$ term ...
- 1,783
2
votes
1
answer
130
views
Definition of symmetry factor $p$ in Feynmans diagrams symmetry factor in Coleman's "Introduction to Many-Body Physics"
I'm trying to digest Coleman's 7.2.1 chapter about symmetry factors. Everything is clear up to point 4 where he introduces symmetry factor $p$ as the "dimension of the group of permutations under ...
- 155
2
votes
1
answer
265
views
D'Alembert operator interaction term in QFT Lagrangian
I'm trying to understand how to find the Feynman rules (and use them to calculate loop diagrams) for this Lagrangian (found on the Saclay lectures):
$$\mathcal{L}=\mathcal{L}_\text{kin}-\frac{\tilde{...
- 5,931
2
votes
0
answers
117
views
Are these two Feynman diagrams different?
I am a little confused about the symmetry of Feynman diagrams. As far as I understand, Feynman diagrams are not symmetric with respect to exchange of external points or momentums if the diagrams are ...
- 1,747
5
votes
2
answers
318
views
Symmetry factors in two interacting fields
Red and blue colored lines represent the two different fields.
At 1st order, by the exchange of the blue legs and red legs we get $\frac{1}{4}$ factor and in one of the 2nd order term drawn above, ...
- 3,464
3
votes
1
answer
312
views
Disconnected Feynman Diagram Combinatorics Factor
Many sources, e.g. these questions (Proof of Connected Diagrams, Most general Feynman diagram) say that the amplitude for a disconnected Feynman diagram is given by $$D = \prod_{i}\frac{1}{n_i!}{C_i}^{...
- 2,604
4
votes
1
answer
1k
views
Definition and proof of Symmetry Factor of Feynman Diagram
Studying QFT, I was told that symmetry factor is defined by:
if there are $m$ ways of arranging vertices and propagators to give identical parts of a diagram (keeping the outer ends of external lines ...
- 1,734
2
votes
0
answers
263
views
Symmetry Factor for Feynman diagram of complex field
When studying Feynman diagram I have been told that when treating a complex scalar field we use pertubation which is normalize with factor $1/n$ (where $n$ is the number of terms in the perturbation) ...
- 1,734