Symmetry factor of a Wick diagram

In summary, The conversation is about the symmetry factor of a Wick diagram in the book Quantum Field for mathematician. The diagram involves a hermitian field interacting with a complex field and has a symmetry factor of 2. The person is confused about this and asks for clarification, stating that they have read about symmetry factors on Wikipedia but still do not understand. The expert responds by explaining that there are two automorphisms of the diagram, one for "a" and one for "d". They further clarify that "d" is not a complex propagator loop and can only be mapped to itself due to the hermitian propagator loop attached. This results in a symmetry factor of 2. The person then asks about the symmetry factor of
  • #1
pscplaton
6
1
Hello !

In the book Quantum Field for mathematician, there is this Wick diagram as an example to understand how to compute the symmetry factor (I am sorry, I draw it with paint...)

wick diagram.png


This is about a hermitian field interacting with a complex field. The book says it has a symmetry factor of 2 but I don't understand why, even after reading about symmetry factor on wikipedia (http://en.wikipedia.org/wiki/Feynman_diagram#Symmetry_factors). I don't see what are the two automorphisms of this Feynman diagram... As far as I understand, for a given automorphism, "a" can only be mapped to "a" because of the complex field loop, and the same applies for "d". "c" cannot be mapped to "b" because it has incoming complex propagator from "a", which is not the case of "b"...

Where am I wrong ?

Thanks!
 
Physics news on Phys.org
  • #2
d is not a complex propagator loop, it has no arrow.
 
  • #3
Yes you are right. I mean that like "a", "d" can only be mapped to itself, because it has a hermitian propagator loop attached, and this is the only hermitian propagator loop of the diagram
 
  • #4
This is the point, you can make the symmetry transformation of changing the direction of this loop without changing the diagram. Hence a symmetry factor of 2.
 
  • #5
Thanks for your reply.

But then I don't understand why the double bubble diagram has a symmetry factor of 2.
bubble.png

According to what you are saying, it should have a symmetry factor of 4, shouldn't it ?

edit: Sorry I was confused. It works. There is actually a symmetry factor of 8
 
Last edited:

What is the symmetry factor of a Wick diagram?

The symmetry factor of a Wick diagram is a number that represents the number of ways in which the diagram can be rearranged without changing its overall structure or value.

Why is the symmetry factor important in Wick diagrams?

The symmetry factor is important because it helps simplify the calculation of amplitudes in quantum field theory. By taking the symmetry factor into account, we can avoid overcounting or undercounting certain terms in the calculation.

How is the symmetry factor calculated?

The symmetry factor is calculated by counting the number of ways in which the external lines of a Wick diagram can be connected without changing the overall structure. This number is then divided by the total number of possible ways to connect the external lines without any restrictions.

What is the relationship between the symmetry factor and the Feynman rules?

The symmetry factor is directly related to the Feynman rules, which are used to calculate amplitudes in quantum field theory. The symmetry factor helps adjust the amplitudes calculated using the Feynman rules to account for the symmetries of the Wick diagram.

How does the symmetry factor affect the final amplitude of a Wick diagram?

The symmetry factor affects the final amplitude of a Wick diagram by adjusting the contribution from each diagram to account for the number of ways it can be rearranged. A larger symmetry factor means a larger contribution to the final amplitude, while a smaller symmetry factor means a smaller contribution.

Similar threads

A Renormalisation of the Fermionic triangle loop
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
I No "i" in the Triple gluon vertex Feynman Rule
    • High Energy, Nuclear, Particle Physics
Replies
8
Views
2K
I Symmetry factor via Wick's theorem
    • High Energy, Nuclear, Particle Physics
Replies
5
Views
2K
A Two loop Feynman diagram with quartic vertex
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
A Question about S(3) spontaneous symmetry breaking in Peskin & Schroeder
    • High Energy, Nuclear, Particle Physics
Replies
4
Views
1K
A How does one find the Feynman diagrams?
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
2K
How to calculate symmetry factor of Feynman graphs?
    • High Energy, Nuclear, Particle Physics
Replies
2
Views
8K
Order of the symmetry group of Feynman Diagrams
    • High Energy, Nuclear, Particle Physics
Replies
2
Views
1K
Symmetry factor of a general Feynman diagram
    • High Energy, Nuclear, Particle Physics
Replies
1
Views
3K
Symmetry factors of some diagrams
    • High Energy, Nuclear, Particle Physics
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top