Recursion and Growth Estimates in Renormalizable Quantum Field Theory
نویسندگان
چکیده
In this paper we show that there is a Lipatov bound for the radius of convergence for superficially divergent one-particle irreducible Green functions in a renormalizable quantum field theory if there is such a bound for the superficially convergent ones. The radius of convergence turns out to be min{ρ, 1/b1}, where ρ is the bound on the convergent ones, the instanton radius, and b1 the first coefficient of the β-function. 1. The set-up 1.
منابع مشابه
Simple recursion relations for general field theories
On-shell methods offer an alternative definition of quantum field theory at treelevel, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a coverin...
متن کاملNew mathematical structures in renormalizable quantum field theories
Computations in renormalizable perturbative quantum field theories reveal mathematical structures which go way beyond the formal structure which is usually taken as underlying quantum field theory. We review these new structures and the role they can play in future developments. PACS classification: 11.10Gh 11.15Bt 11.10Jj
متن کاملFeynman amplitudes in renormalizable non-commutative quantum field theory
We consider here the Feynman amplitudes of renormalizable non-commutative quantum field theory models. Different representations (the parametric and the Mellin one) are presented. The latter further allows the proof of meromorphy of a amplitude in the space-time dimension.
متن کاملInfinite Reduction Of Couplings In Non-Renormalizable Quantum Field Theory
I study the problem of renormalizing a non-renormalizable theory with a reduced, eventually finite, set of independent couplings. The idea is to look for special relations that express the coefficients of the irrelevant terms as unique functions of a reduced set of independent couplings λ, such that the divergences are removed by means of field redefinitions plus renormalization constants for t...
متن کاملar X iv : h ep - t h / 06 05 09 6 v 1 9 M ay 2 00 6 An Étude in non - linear Dyson – Schwinger Equations ∗
We show how to use the Hopf algebra structure of quantum field theory to derive nonperturbative results for the short-distance singular sector of a renormalizable quantum field theory in a simple but generic example. We discuss renormalized Green functions GR(α,L) in such circumstances which depend on a single scale L = ln q /μ and start from an expansion in the scale GR(α,L) = 1 + ∑ k γk(α)L ....
متن کامل