Stevenson P. Renormalized Perturbation Theory And Its Optimization...2022 torrent

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The results of renormalized perturbation theory, in QCD and other quantum field theories, are ambiguous at any finite order, due to renormalization-scheme dependence. The perturbative results depend upon extraneous scheme variables, including the renormalization scale, that the exact result cannot depend on. Such 'non-invariant approximations' occur in many other areas of physics, too. The sensible strategy is to find where the approximant is stationary under small variations of the extraneous variables. This general principle is explained and illustrated with various examples. Also dimensional transmutation, RG equations, the essence of renormalization and the origin of its ambiguities are explained in simple terms, assuming little or no background in quantum field theory. The minimal-sensitivity approach leads to 'optimized perturbation theory,' which is developed in detail. Applications to Re⁺e⁻, the infrared limit, and to the optimization of factorized quantities, are also discussed thoroughly.
Introduction
Renormalization and Its Ambiguities
Dimensional Analysis in Quantum Field Theory
Renormalization as Reparametrization
Non-invariant Approximations and the Principle of Minimal Sensitivity
Induced Convergence
Optimized Perturbation Theory
Preliminaries: RG Invariance, int-β Equation, Λ Definition, and CG Relation
Parametrization of RS Dependence and the ρn Invariants
Finite Orders and Optimization
Solution for the Optimized rm Coefficients and Optimization Algorithm
Numerical Examples for Re+e− in QCD
Special Topics
Infrared Limit: Fixed and Unfixed Points
Optimization of Factorized Quantities
Exploring All-Orders OPT in the Small-b (BZ) Limit