Is the analytic properties of Fermionic self energy well known?

In summary, For Fermionic self energies with arbitrary wn, the real part is always even and the imaginary part is always odd. This property is well known and often used in calculations.
  • #1
bsmile
48
2
For arbitrary Fermionic self energy, \Sigma(i wn) with wn=(2n+1)pi T, its real part is always an even function of wn while its imaginary part is always an odd function of wn.
 
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  • #2
I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
 
  • #3
Sorry, I think the issues about this analytic property of self energy is well known, or easily derived. I was curious why people would not enforce it in their calculation when say they design self energy ansatz for possible analytic continuation.
 
  • #4
Or, more specifically, \sigma(iw)=\sigma(-iw)*
 

1. What is the Fermionic self energy?

The Fermionic self energy is a mathematical concept in quantum field theory that describes the interaction between a fermion (a particle with half-integer spin) and its surrounding environment. It is also known as the fermion's mass correction or the fermion's self-mass.

2. Why is understanding the analytic properties of Fermionic self energy important?

Understanding the analytic properties of Fermionic self energy is crucial in studying the behavior and interactions of fermions in quantum field theory. It also allows for more accurate calculations and predictions in particle physics experiments.

3. What are the analytic properties of Fermionic self energy?

The analytic properties of Fermionic self energy refer to its behavior and mathematical properties in the complex plane. These include its poles, which correspond to the mass and lifetime of the fermion, and its branch cuts, which indicate the energy range in which the fermion can exist.

4. Is the analytic properties of Fermionic self energy well known?

Yes, the analytic properties of Fermionic self energy are well known and extensively studied in the field of quantum field theory. They have been confirmed through various experiments and calculations, and are an important aspect in the Standard Model of particle physics.

5. How do scientists study the analytic properties of Fermionic self energy?

Scientists study the analytic properties of Fermionic self energy through theoretical calculations and experiments, such as particle collider experiments. They also use mathematical techniques, such as perturbation theory and renormalization, to analyze and understand the behavior of the self energy function.

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