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On the Ward Identities for the Hubbard Model. Particle‐Number Conservation and the Analytical Structure of the Self‐Energy
Author(s) -
Behn U.
Publication year - 1978
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220880237
Subject(s) - hubbard model , physics , limit (mathematics) , conservation law , spin (aerodynamics) , conservation of energy , particle (ecology) , particle number , electron , point particle , point (geometry) , energy conservation , statistical physics , classical mechanics , quantum mechanics , mathematics , mathematical analysis , geometry , ecology , superconductivity , plasma , biology , thermodynamics
The Ward identities for the Hubbard model connected with the spin‐rotational invariance and the particle‐number conservation are derived considering the equation of motion for 4‐point Green functions. Exploiting the generalized Ward identity connected with the particle‐number conservation, the self‐energy splits into a static part and a dynamic part. The latter describes the effects due to the hopping of the electrons of the opposite spin. The analytical structure which guarantees the particle‐number conservation and the reproduction of the atomic limit, can explicitely be seen so that approximations may be performed conserving this structure.