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Regularity of the moving Fermi surface: RPA contributions
Author(s) -
Feldman Joel,
Salmhofer Manfred,
Trubowitz Eugene
Publication year - 1998
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199809/10)51:9/10<1133::aid-cpa8>3.0.co;2-e
Subject(s) - fermi surface , fermi gamma ray space telescope , gravitational singularity , renormalization , tangent , mathematics , mathematical proof , surface (topology) , fermi energy , physics , quantum mechanics , mathematical physics , mathematical analysis , geometry , superconductivity , electron
Regularity of the deformation of the Fermi surface under short‐rangeinteractions is established for all contributions to the RPAself‐energy (it is proven in an accompanying paper that the RPAgraphs are the least regular contributions to the self‐energy).Roughly speaking, the graphs contributing to the RPA self‐energy arethose constructed by contracting two external legs of a four‐leggedgraph that consists of a string of bubbles. This regularity is anecessary ingredient in the proof that renormalization does notchange the model. It turns out that the self‐energy is more regularwhen derivatives are taken tangentially to the Fermi surface thanwhen they are taken normal to the Fermi surface. The proofs requirea very detailed analysis of the singularities that occur at thosemomenta p where the Fermi surface S is tangent to S + p .Models in which S is not symmetric under the reflection p → − p are included. © 1998 John Wiley & Sons, Inc.