Annales Henri Poincaré

, Volume 20, Issue 7, pp 2323–2352 | Cite as

Generating Functions for Lattice Gauge Models with Scaled Fermions and Bosons

  • Paulo A. Faria da VeigaEmail author
  • Michael O’Carroll


Recently, employing an imaginary-time functional integral formulation, we considered abelian and nonabelian \((a{\mathbb {Z}})^d\) lattice quantum field gauge theories with new a-dependent locally scaled Wilson Fermi and Bose fields in \(d\le 4\) spacetime dimensions and neglecting the pure gauge interaction. The use of scaled fermions and bosons preserves Osterwalder–Schrader positivity and the spectral content of the models since the decay rates of correlations in the infinite-time limit are unchanged. In addition, scaled fields also result in a less singular, more regular behavior in the continuum limit. The scaled field gauge models are thermodynamically stable, which shows that stability does not depend on the presence of a pure gauge, plaquette term in the action. The finite lattice free energy is bounded with a bound independent of the number of points of the lattice and the lattice spacing \(a\in (0,1]\). Recall that the expansion of the fermionic exponential bond factor, arising from the interacting nearest neighbor hopping terms in the action, is finite by Pauli exclusion. The Bose-Gauge models we consider here have a finite truncation of the bond factor; the Fermi-mimicking truncated Bose models still obey Osterwalder–Schrader positivity. We show boundedness of the n-point scaled field generating functions and n-point scaled field correlations. The bounds are independent of the number of lattice points and the lattice spacing \(a\in (0,1]\). For the truncated Bose models, the bound is also independent of the location of the n points. No renormalization of the parameters is needed. The precise a-dependent factors have been extracted and isolated from the unscaled field partition functions and correlations so that the scaled field free energies and correlations are not singular for \(a\in (0,1]\).



We thank FAPESP and CNPq for support and the referees for valuable suggestions.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Paulo A. Faria da Veiga
    • 1
    Email author
  • Michael O’Carroll
    • 1
  1. 1.Departamento de Matemática Aplicada e Estatística - ICMCUSP-São CarlosSão CarlosBrazil

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