Tadpole graph & normal ordering

In summary, the conversation discussed the elimination of the tadpole graph from perturbation expansion through the adoption of normal-ordered interaction. The question was raised about how this can be proven and if there are any references available. The response provided a brief explanation of why the tadpole for the photon must vanish in QED and how the specific diagram mentioned in the conversation also vanishes through direct computation. These two statements are related.
  • #1
QuantumDevil
29
0
It is said that so called tadpole graph gets eliminated from perturbation expansion if the normal-ordered interaction is adopted. How can it be proved? Can anybody provide some links or any other references about this problems?

[tex]L_{int}=-e:\bar{\psi}\gamma_{\mu}\psi A^{\mu}:[/tex]
 
Last edited:
Physics news on Phys.org
  • #2
Here is attachement with this graph
 

Attachments

  • tadpole.jpg
    tadpole.jpg
    3.3 KB · Views: 680
  • #3
...and this also should remove the mass shift I suppose.
 
  • #4
See Peskin and Schroder, Chapter 4.

You can see right away that (at least in QED) tadpoles for the photon must vanish, since QED has a charge-conjugation symmetry in which the photon field is odd, so the one-point function for the photon must vanish. You can also see that the diagram you included vanishes since the loop integral explicitly vanishes:

[tex]\int d^4k\frac{{\rm Tr}[\gamma^\mu(k\!\!\!\slash+m)]}{k^2-m^2}= \int d^4k\frac{4k^\mu+0}{k^2-m^2}=0[/tex]

These two statements are, of course, related.
 
  • #5
How do you know that it is zero by direct computation?
 

FAQ: Tadpole graph & normal ordering

What is a Tadpole graph?

A Tadpole graph is a type of graph in the field of mathematics and physics that is used to represent a particular mathematical expression. It is characterized by a loop that connects two vertices and is typically drawn as a circle with a tail.

What is normal ordering in physics?

Normal ordering is a mathematical technique used in quantum field theory to rearrange the terms in an expression for a quantum operator in a specific way. This is done to ensure that the operator has the correct symmetries and properties.

How is a Tadpole graph used in physics?

In physics, Tadpole graphs are used to represent Feynman diagrams, which are graphical representations of mathematical expressions that describe the behavior of subatomic particles. These diagrams are used to calculate the probabilities of various particle interactions.

What is the significance of normal ordering in quantum mechanics?

In quantum mechanics, normal ordering is important because it helps to eliminate divergences in calculations involving quantum operators. It also ensures that the operator has the correct symmetries and properties, which are essential for accurate calculations.

What are the challenges in dealing with Tadpole graphs and normal ordering?

One of the main challenges in dealing with Tadpole graphs and normal ordering is the complexity of the calculations involved. The equations and diagrams can become very complicated, and it requires a deep understanding of mathematics and physics to accurately analyze them.

Similar threads

Replies
6
Views
1K
Replies
1
Views
1K
Replies
31
Views
4K
Replies
4
Views
2K
Replies
6
Views
2K
Replies
6
Views
2K
Replies
1
Views
2K
Replies
5
Views
2K
Replies
49
Views
4K
Back
Top