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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.
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.
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.
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.
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.
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.