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oapen-20.500.12657-608892024-03-27T14:15:07Z Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity Stevenson, P.M. Physics;Particle Physics / High Energy Physics / Quantum Fields thema EDItEUR::P Mathematics and Science::PG Astronomy, space and time::PGK Cosmology and the universe 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. 2023-01-26T10:14:25Z 2023-01-26T10:14:25Z 2022 book 9789811255687 9789811255700 https://library.oapen.org/handle/20.500.12657/60889 eng application/pdf Attribution-NonCommercial 4.0 International 9789811255694.pdf World Scientific Publishing Company World Scientific 10.1142/12817 10.1142/12817 af1172b5-c0c7-4a09-866a-f0f09d9798ec 9789811255687 9789811255700 World Scientific 296 Singapore open access
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OAPEN
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English
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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.
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World Scientific Publishing Company
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2023
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1799945262627553280
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