Functional integrals and diagram techniques for Fermi particles

Victor Nikolaevich Popov

Victor Nikolaevich Popov

Part I. Functional Integrals and Diagram Techniques in Statistical Physics: Part II. Superfluid Bose Systems: Part III. Plasma and Superfluid Fermi Systems: Part IV. Crystals, Heavy Atoms, Model Hamiltonians.

Wolfgang Weller, M. Souleiman, Winfried Kolley +1 more

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.

Joel Feldman, Horst Knörrer, Eugene Trubowitz B

Yu. A. Izyumov, Felix A. Kassan-Ogly, Yu. N. Skryabin

A diagram technique for calculation of correlation functions of ferromagnet being described by the Ising model is proposed here and its zero approximation corresponds to the selfconsistent field. The essential dependence of a numerical factor of a diagram upon its structure is the important peculiarity of this technique in comparison with the usual diagram technique for fermion or boson operators. It leads to the special character of analytical series corresponding to the certain diagram series and to the special ways of their summarizing. The exact forma1 expression for the average spontaneous moment in terms of irreducible many-particle correlation functions had been obtained. A certain series of graphs for spontaneous moment which corresponds to the Gaussian fluctuations of the selfconsistent field being taken into account had been extracted. A relation between the proposed diagram technique and the expansion of functional integrals for the correlation functions of the Ising model had been obtained as well. In conclusion the referencies to authors papers where a diagram technique for Heisenberg and s-d models are developed are given there.