Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Annalen der Physik

On Generating Functionals for Interacting Disordered Fermi Systems without Denominators

Wolfgang Weller, M. Souleiman, Winfried Kolley, Marcus Kasner

Published Jan 1, 1990• 0 citations
Publisher

Abstract

Abstract For a disordered Fermi System the generating functional for Green functions in Keldysh technique is represented as a functional integral in a time/frequency lattice. The normalization denominator is rigorously shown to be equal to 1. Rules for the diagram analysis are given reducing the multi‐frequency scheme to the external frequencies.

DOI
10.1002/andp.19905020224

Related papers

A new field-theoretical formulation for the motion of an electron in a quenched disorder potential

Wolfgang Weller, Frank Stefani, M. Souleiman

Following a proposal by Aronov and Ioselevich, we express the Green functions (GF) of a noninteracting disordered Fermi system as a functional integral on a real time/frequency lattice. The normalizing denominator of this functional integral is equal to unity, because of identities satisfied by the GF. The GF can then be simply averaged with respect to the random disorder potential. We describe the fermionic fields not belonging to the external frequency by means of a bosonic auxiliary field g. The Hubbard-Stratonovich field Q is introduced only with respect to the fermionic fields for the external frequency.

arXiv:cond-mat/9606185•Jun 25, 1996•0 citations

Path integral scheme on a flexible time contour for random electron models

E. Kolley, Winfried Kolley

A field-theoretic time path approach to an interacting electron system with quenched site randomness is extended to a one-parameter variety of contours. The average generating functional for real-time finite-temperature Green functions is deduced. Propagators along the Keldysh contour and the Niemi-Semenoff contour are included as special cases.

Journal of Physics A Mathematical and General•Mar 21, 1988•1 citation

A new functional integral formalism for strongly correlated Fermi systems

S K Sarker

A new functional integral mapping of a strongly correlated Fermi system to another Fermi system is presented. The strong correlations appear in the new system through momentum- and frequency-dependent coupling constants characterising correlated multi-particle motions, which can be treated perturbatively. The method is well suited to treat Hubbard and Anderson models. For the Hubbard model, the lowest-order term reproduces Hubbard's two-band Green function. Second-order processes leading to spin fluctuations are identified.

Journal of Physics C Solid State Physics•Jun 30, 1988•15 citations

Green's function technique and the quasiparticles approach in normal metals: two classical results

Pedro Contreras

A review of relevant ideas in the quasiparticle picture in normal Fermi systems based on the phenomenological approach given by Landau to the electrons in a metal is made. The methods of Feynman diagrams and Green’s function technique for T=0 case are introduced in the example of the quasiparticle lifetime in a normal Fermi system. Therefore, the way to obtain the spectrum of the quasiparticles and collective excitations in a free Fermi gas as well as in an external weak field are discussed. As concluding point in this part, the lifetime of Landau quasiparticles is calculate. The second part deals with the so called Matsubara technique which applies to systems above T=0. Also the so called Edward’s technique of drawing the Feynman diagrams in presence of random impurities potential is discussed. and the influence of such a field for a system of Fermi particles that undergoes the influence of a external prove such as the electrical field is studied by calculating the electrical DC conductivity and showing what kind of scattering its important in this case.

•Jan 1, 2001•0 citations

Generating functional for closed time-path green functions of disordered fermion systems

E. Kolleyd, W. Kolleyd

Physics Letters A•Oct 1, 1987•5 citations

Feynman Diagrams and External Potentials

Henrik Bruus, Karsten Flensberg

Abstract From the previous chapters on linear response theory and Green’s functions, it is clear that complete calculations of thermal averages of time-dependent phenomena in quantum field theory are a rather formidable task. Even the basic imaginary time-evolution operator Û (τ ) itself is an infinite series to all orders in the interaction Û(ϊ) . One simply faces the problem of getting lost in the myriads of integrals, and not being able to maintain a good physical intuition of which terms are important. In 1948 Feynman solved this problem as part of his seminal work on quantum electrodynamics by inventing the ingenious diagrams that today bear his name. The Feynman diagrams are both an exact mathematical representation of perturbation theory to infinite order and a powerful pictorial method that elucidate the physical content of the complicated expressions. In this chapter, we introduce the Feynman diagrams for the case of non-interacting particles in an external potential. Our main example of their use will be the analysis of electron-impurity scattering in disordered metals.

•Sep 2, 2004•0 citations
Abstract For a disordered Fermi System the generating functional for Green functions in Keldysh technique is represented as a functional integral in a time/frequency lattice. The normalization denominator is rigorously shown to be equal to 1. Rules for the diagram analysis are given reducing the multi‐frequency scheme to the external frequencies.
Following a proposal by Aronov and Ioselevich, we express the Green functions (GF) of a noninteracting disordered Fermi system as a functional integral on a real time/frequency lattice. The normalizing denominator of this functional integral is equal to unity, because of identities satisfied by the GF. The GF can then be simply averaged with respect to the random disorder potential. We describe the fermionic fields not belonging to the external frequency by means of a bosonic auxiliary field g. The Hubbard-Stratonovich field Q is introduced only with respect to the fermionic fields for the external frequency.
A new functional integral mapping of a strongly correlated Fermi system to another Fermi system is presented. The strong correlations appear in the new system through momentum- and frequency-dependent coupling constants characterising correlated multi-particle motions, which can be treated perturbatively. The method is well suited to treat Hubbard and Anderson models. For the Hubbard model, the lowest-order term reproduces Hubbard's two-band Green function. Second-order processes leading to spin fluctuations are identified.
A review of relevant ideas in the quasiparticle picture in normal Fermi systems based on the phenomenological approach given by Landau to the electrons in a metal is made. The methods of Feynman diagrams and Green’s function technique for T=0 case are introduced in the example of the quasiparticle lifetime in a normal Fermi system. Therefore, the way to obtain the spectrum of the quasiparticles and collective excitations in a free Fermi gas as well as in an external weak field are discussed. As concluding point in this part, the lifetime of Landau quasiparticles is calculate. The second part deals with the so called Matsubara technique which applies to systems above T=0. Also the so called Edward’s technique of drawing the Feynman diagrams in presence of random impurities potential is discussed. and the influence of such a field for a system of Fermi particles that undergoes the influence of a external prove such as the electrical field is studied by calculating the electrical DC conductivity and showing what kind of scattering its important in this case.
Abstract From the previous chapters on linear response theory and Green’s functions, it is clear that complete calculations of thermal averages of time-dependent phenomena in quantum field theory are a rather formidable task. Even the basic imaginary time-evolution operator Û (τ ) itself is an infinite series to all orders in the interaction Û(ϊ) . One simply faces the problem of getting lost in the myriads of integrals, and not being able to maintain a good physical intuition of which terms are important. In 1948 Feynman solved this problem as part of his seminal work on quantum electrodynamics by inventing the ingenious diagrams that today bear his name. The Feynman diagrams are both an exact mathematical representation of perturbation theory to infinite order and a powerful pictorial method that elucidate the physical content of the complicated expressions. In this chapter, we introduce the Feynman diagrams for the case of non-interacting particles in an external potential. Our main example of their use will be the analysis of electron-impurity scattering in disordered metals.