Feynman diagrams for Bremsstrahlung

In summary, we discussed the breaking radiation emitted by the scattering of an electron with an external field, described by a Hamiltonian. At the second order, the interaction between the electron, the external field, and the quantized field is taken into account using time-ordered and normal products. Although Feynman diagrams only show the leading contributions, the expression for the breaking radiation at the second order considers higher order contributions.
  • #1
eoghan
207
7
Hi,

the breaking radiation emitted by the scattering of an electron with an external field is described by the hamiltonian:
[tex]
H=\bar \Psi^- (\displaystyle{\not}{A}_e + \displaystyle{\not}A) \Psi^+
[/tex]
where [itex]A_e[/itex] is the external static classical field, while [itex]A[/itex] is the quantized field.
The breaking radiation at the second order is given by (up to some constants):
[tex]
S^{(2)}=\int d^4 x_1 d^4 x_2 T \{ N [ \bar \Psi^- (\displaystyle{\not}{A}_e + \displaystyle{\not}A) \Psi^+ ]_{x_1} N[\bar \Psi^- (\displaystyle{\not}{A}_e + \displaystyle{\not}A) \Psi^+] _{x_2}\}
[/tex]
where T is the time-ordered product and N is the normal product.
If I contract the two fermion fields (e.g. [itex]\bar \Psi^- (x_1)[/itex] with [itex]\Psi^+ (x_2)[/itex] I get that in both x1 and x2 there is the interaction between an electron, the external field and the quantized field. But in all the feynman diagrams I saw, in x1 there is only the interaction between the electron and the external field, whereas in x2 there is only the interaction between the electron and the quantized field... how can this be possible?
 
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  • #2


Hello,

Thank you for bringing up this interesting topic. The breaking radiation emitted by the scattering of an electron with an external field is indeed described by the Hamiltonian you mentioned. This Hamiltonian takes into account the interaction between the electron, the external field, and the quantized field.

In the expression for the breaking radiation at the second order, we see the use of time-ordered product and normal product. This is because at the second order, we have to consider the interaction between the electron and the external field at both x1 and x2. The time-ordered product takes into account the temporal ordering of these interactions, while the normal product takes care of the anti-commutation relations of the fermion fields.

Now, you are right in pointing out that in the Feynman diagrams, we only see the interaction between the electron and the external field at x1 and the interaction between the electron and the quantized field at x2. This is because the Feynman diagrams represent only the leading contributions to the scattering process. Higher order contributions, which are taken into account in the expression for the breaking radiation at the second order, are not shown in the Feynman diagrams.

I hope this clarifies your doubt. Please let me know if you have any further questions.
 

1. What is a Feynman diagram for Bremsstrahlung?

A Feynman diagram for Bremsstrahlung is a graphical representation of the interaction between an electron and a nucleus, where the electron loses energy and emits a photon. It is used to visualize and calculate the probability of this type of radiation occurring.

2. How do Feynman diagrams for Bremsstrahlung work?

Feynman diagrams for Bremsstrahlung follow a set of rules and conventions to represent the interaction between particles. The diagram consists of straight lines representing particles, wavy lines representing photons, and vertices where the particles interact. The direction of the lines and the position of the vertices determine the probability of the interaction occurring.

3. What is the significance of Bremsstrahlung in physics?

Bremsstrahlung, also known as braking radiation, is an important phenomenon in physics as it is one of the ways in which particles can lose energy. It is also used in various fields such as medical imaging and particle accelerators.

4. What are the limitations of Feynman diagrams for Bremsstrahlung?

One limitation of Feynman diagrams for Bremsstrahlung is that they only represent the lowest order of interaction between particles. They do not take into account higher-order interactions, which can be important in certain scenarios. Additionally, the calculations from Feynman diagrams can become complicated for interactions involving more than two particles.

5. How are Feynman diagrams for Bremsstrahlung used in research?

Feynman diagrams for Bremsstrahlung are used in theoretical research to make predictions about the behavior of particles in various interactions. They are also used in experimental research to compare with data and validate theoretical models. Additionally, they are used in the development of new technologies and applications such as particle accelerators and medical imaging techniques.

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