# Photon self-energy in the finite temperature field theory (real -time)

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• Tian
In summary, the conversation discussed difficulties with reading formulae and evaluating tadpole diagrams in a physics context. The initial expression was deemed correct with a possible sign difference between vertices. The use of three and four momentum was also mentioned.
Tian
TL;DR Summary
I want to calculate photon selfenergy in the finite temperature field theory (real -time). There are two delta function. There may be some wrong in my calculation ,but I can not find it

Your formulae are hard to read, but as far as I can see, the initial expression looks correct (maybe up to a sign, because the +-vertex has the opposite sign of the --vertex; the additional - from the fermion loop is, of course, correct).

The only place, where you have trouble with the ##\delta## functions is in the evaluations of tadpole diagrams (i.e., loops beginning and ending at the same vertex).

Tian
Thank you very much , the note maybe hard to read . I should distinguish between three momentum and four momentum. Capital letters represent four momentum, and small letters represent three momentum. I hope you can see my note again. This probelm confused me long time .

And you are right, there is a sign problem, but I don't know the mean of “ the +-vertex has the opposite sign of the --vertex”

That's because one branch of the contour is in positive and the other in negative time direction. It depends on your convention which one you call the plus and which one the minus-branch.

## 1. What is photon self-energy in the finite temperature field theory?

Photon self-energy is a concept in quantum field theory that describes the interactions between photons and other particles in a system at a finite temperature. It is a measure of how the energy of a photon changes due to its interactions with other particles in the system.

## 2. How is photon self-energy calculated in real-time?

In real-time calculations, photon self-energy is typically calculated using a technique called the Feynman diagram approach. This involves representing the interactions between particles using diagrams and using mathematical equations to calculate the resulting self-energy.

## 3. What is the significance of photon self-energy in finite temperature field theory?

Photon self-energy is important in understanding the behavior of particles in a system at a finite temperature. It can affect the properties of particles, such as their mass and energy, and can also influence the dynamics of the system as a whole.

## 4. How does photon self-energy change at different temperatures?

At higher temperatures, the interactions between particles in a system become more frequent and intense, leading to a greater impact on the self-energy of photons. As a result, the self-energy of photons can change significantly at different temperatures.

## 5. Can photon self-energy be measured experimentally?

Yes, photon self-energy can be indirectly measured through experiments that observe the properties of particles in a system. By comparing the predicted values of self-energy with experimental data, scientists can validate the theories and calculations used to describe finite temperature field theory.

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