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DY: Fachverband Dynamik und Statistische Physik

DY 54: Statistical Physics: General II

DY 54.6: Vortrag

Donnerstag, 12. März 2026, 16:15–16:30, ZEU/0114

Fermion as a non-local particle-hole excitation — •Girish Setlur — Department of Physics, Indian Institute of Technology Guwahati

We show that the fermion, in the context of a system that comprises many such entities, which, by virtue of the Pauli exclusion principle, possesses a Fermi surface at zero temperature, may itself be thought of as a collection of non-local particle-hole excitations across this Fermi surface. This result is purely kinematical and completely general, not restricted to any specific dimension, and is applicable to both continuum and lattice systems. There is also no implication that it is applicable only to low-energy phenomena close to the Fermi surface. We are able to derive the full single-particle dynamical Green function of this fermion at finite temperature by viewing it as a collection of these non-local particle-hole excitations. The Green function of the fermion then manifests itself as a solution to a first-order differential equation in a parameter that controls the number of particle-hole pairs across the Fermi surface, and this equation itself reveals variable coefficients that may be identified with a Bose-Einstein distribution, implying that there is a sense in which the non-local particle-hole excitations have bosonic qualities while not being exact bosons at the level of operators. We also recall the definition of the non-local particle-hole operator that may be used to diagonalize the kinetic energy of free fermions of the sort mentioned above. Number-conserving products of creation and annihilation operators of fermions are expressible as a (rather complicated) combination of these non-local particle-hole operators.

Keywords: Fermions, Green functions