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

P. A. Faria da Veiga
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P. A. Faria da Veiga: Harvard University, Department of Mathematics

A chapter in Mathematical Physics X, 1992, pp 420-422 from Springer

Abstract: 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.

Keywords: Fredholm Determinant; Boson Field; Lead Order Approximation; Perturbative Renormalizability; Intermediate Boson (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-3-642-77303-7_46

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