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Il Nuovo Cimento (1955-1965)

, Volume 15, Issue 6, pp 959–969 | Cite as

Canonical transformation and perturbation expansion in the theory of Fermi gas

Article

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.

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References

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Copyright information

© Società Italiana di Fisica 1960

Authors and Affiliations

  • G. Fano
    • 1
  1. 1.Istituto Nazionale di Fisica NucleareSezione di BolognaItaly

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