Summary
A canonical transformation, identical with that of Bogoljubov and Valatin, is performed; and a perturbation expansion of the ground state energy is made by taking, as the unperturbed Hamiltonian, the term describing free « quasi particles ». The perturbation is written in normal form: it follows that the canonical transformation cancels, to all orders, diagrams containing lines with the two end points at the same vertex. A simple discussion of the ground state energy is given in the case considered by the theory of Bardeen, Cooper and Schrieffer.
Riassunto
Viene eseguita una trasformazione canonica, identica a quella di Bogoljubov e Valatin; viene eseguito inoltre uno sviluppo perturbativo dell’energia dello stato fondamentale, prendendo come Hamiltoniana imperturbata il termine che descrive « quasi particelle » libere. La perturbazione viene scritta in forma normale: ne segue che la trasformazione canonica cancella, a tutti gli ordini, diagrammi contenenti linee che escono ed entrano dallo stesso vertice. È svolta inoltre una semplice discussione sul valore dell’energia dello stato fondamentale nel caso considerato dalla teoria di Bardeen, Cooper e Schrieffer.
Similar content being viewed by others
References
J. Bardeen, L. Cooper andJ. R. Schrieffer:Phys. Rev.,108, 1175 (1957).
N. N. Bogoljubov:Nuovo Cimento,7, 794 (1958).
N. N. Bogoljubov, V. V. Tolmachev andD. V. Shirkov:A New Method in the Theory of Superconductivity (Moscow, 1958).
J. G. Valatin:Nuovo Cimento,7, 843 (1958).
S. T. Beliaev:Introduction to the Bogoljubov Canonical Transformation Method. Cours données a l’école d’été de physique théorique (Les Houches, Session 1958):Le problème a N corps (New York, 1958).
V. V. Tolmachev andS. V. Tiablikov:Žurn. Ėksp. Teor. Fiz.,34, 46 (1958).
See eq. (15), (16) and (17) of reference (6).
L. Van Hove:Physica,25, 849 (1959).
This variable has been introduced byValatin (reference (4), eq. (3a)) with the symbolξ +k .
F. J. Dyson:Phys. Rev.,82, 428 (1951).
J. Goldstone:Proc. Roy. Soc., A239, 627 (1957).
N. M. Hugenholtz:Physica,23, 481 (1957).
E. R. Caianiello:Nuovo Cimento,10, 1634 (1953).
Author information
Authors and Affiliations
Additional information
This work was performed in part at the Istituto di Fisica Teorica e Nucleare, Naples.
Rights and permissions
About this article
Cite this article
Fano, G. Canonical transformation and perturbation expansion in the theory of Fermi gas. Nuovo Cim 15, 959–969 (1960). https://doi.org/10.1007/BF02860202
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02860202