Journal of Statistical Physics

, Volume 78, Issue 3–4, pp 1067–1082 | Cite as

Orthogonality between scales in a renormalization group for fermions

  • Emmanuel Pereira


Having in mind the development of a technical tool to treat fermionic systems, we propose a Kadanoff-Wilson block renormalization transformation employing unusual averages (an inevitable artifact due to the specificity of lattice fermions and to the desired transformation properties). The free propagator is decomposed into operators associated to different momentum scales and with orthogonal relations, and the effective actions generated from the Dirac operator by the transformations present uniform exponential decay. We argue to show the usefulness of the formalism to study correlation functions of interacting fermions.

Key Words

Orthogonality between scales renormalization group fermions 


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  1. 1.
    K. Gawedzki and A. Kupiainen, Block spin renormalization group for dipole gas and (∇φ)4,Ann. Phys. 147:198–243 (1983).Google Scholar
  2. 2.
    G. Benfatto and G. Gallavotti, Perturbation theory of the Fermi surface in a quantum liquid,J. Stat. Phys. 59(3/4):541–664 (1990).Google Scholar
  3. 3.
    E. Pereira and M. O'Carroll, Orthogonality between scales and wavelets in a representation for correlation functions. The lattice dipole gas and (∇φ)4 models,J. Stat. Phys. 73(3/4):695–721 (1993).Google Scholar
  4. 4.
    M. O'Carroll and E. Pereira, A representation for the generating and correlation functions in the block field renormalization group formalism and asymptotic freedom,Ann. Phys. 218:139–159 (1992).Google Scholar
  5. 5.
    T. Balaban, M. O'Carroll, and R. Schor, Block renormalization group for Euclidean fermions,Commun. Math. Phys. 122:233–247 (1989).Google Scholar
  6. 6.
    A. C. D. Van Enter, R. Fernandez and A. D. Sokal, Renormalization transformations in the vicinity of first-order phase transitions: What can and cannot go wrong,Phys. Rev. Lett. 66:3253–3256 (1991).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Emmanuel Pereira
    • 1
  1. 1.Departamento de Física-ICExUniversidade Federal de Minas GeraisBelo Horizonte MGBrazil

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