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Existence of the Schwinger Functions of the Three-Dimensional Gross-Neveu Model

In: Mathematical Physics X

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  • P. A. Faria da Veiga

    (Harvard University, Department of Mathematics)

Abstract

One of the conclusions of previous rigorous studies on renormalization theory is that the concept of perturbative renormalizability shall not be considered as a fundamental requirement for a quantum field model to exist. Indeed, to solve the question of the ultraviolet (UV) limit, ρ → ∞, of a model presenting a set of parameters Ω ρ [ρ labelling an UV cutoff], in most cases one must drop out completely the traditional intermediate step involving a Taylor expansion in the coupling constant and properly ask whether or not one can prescribe functions for the parameters appearing in Ω ρ , in terms of the variable ρ and the set Ω ren of (finite and often positive) renormalized parameters, such that the n-point Schwinger (correlation) functions S n,ρ exist when ρ → ∞ and describe a non-trivial (interacting) system.

Suggested Citation

  • P. A. Faria da Veiga, 1992. "Existence of the Schwinger Functions of the Three-Dimensional Gross-Neveu Model," Springer Books, in: Konrad Schmüdgen (ed.), Mathematical Physics X, pages 420-422, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-77303-7_46
    DOI: 10.1007/978-3-642-77303-7_46
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