Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity
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 d...
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| Формат: | Online |
| Хэл сонгох: | англи |
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World Scientific Publishing Company
2023
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| Онлайн хандалт: | https://library.oapen.org/handle/20.500.12657/60889 |
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| _version_ | 1869531329665695744 |
|---|---|
| author | Stevenson, P.M. |
| author_browse | Stevenson, P.M. |
| author_facet | Stevenson, P.M. |
| author_sort | Stevenson, P.M. |
| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-96400 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | World Scientific Publishing Company |
| publisherStr | World Scientific Publishing Company |
| record_format | ojs |
| spelling | doab-20.500.12854ir-964002025-07-17T12:15:45Z 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 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. 2023-01-28T04:11:45Z 2023-01-28T04:11:45Z 2023-01-26T10:14:25Z 2022 book https://library.oapen.org/handle/20.500.12657/60889 9789811255687 9789811255700 https://directory.doabooks.org/handle/20.500.12854/96400 eng open access image/jpeg image/jpeg Attribution-NonCommercial 4.0 International Attribution-NonCommercial 4.0 International https://library.oapen.org/bitstream/20.500.12657/60889/1/9789811255694.pdf https://library.oapen.org/bitstream/20.500.12657/60889/1/9789811255694.pdf World Scientific Publishing Company World Scientific 10.1142/12817 10.1142/12817 717c2bee-70cb-4ad9-acf0-903aa40d2096 9789811255687 9789811255700 World Scientific 296 Singapore open access |
| spellingShingle | Physics;Particle Physics / High Energy Physics / Quantum Fields thema EDItEUR::P Mathematics and Science::PG Astronomy, space and time::PGK Cosmology and the universe thema EDItEUR::P Mathematics and Science::PG Astronomy, space and time::PGK Cosmology and the universe Stevenson, P.M. Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity |
| title | Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity |
| title_full | Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity |
| title_fullStr | Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity |
| title_full_unstemmed | Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity |
| title_short | Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity |
| title_sort | renormalized perturbation theory and its optimization by the principle of minimal sensitivity |
| topic | Physics;Particle Physics / High Energy Physics / Quantum Fields thema EDItEUR::P Mathematics and Science::PG Astronomy, space and time::PGK Cosmology and the universe thema EDItEUR::P Mathematics and Science::PG Astronomy, space and time::PGK Cosmology and the universe |
| topic_facet | Physics;Particle Physics / High Energy Physics / Quantum Fields thema EDItEUR::P Mathematics and Science::PG Astronomy, space and time::PGK Cosmology and the universe thema EDItEUR::P Mathematics and Science::PG Astronomy, space and time::PGK Cosmology and the universe |
| url | https://library.oapen.org/handle/20.500.12657/60889 |
| work_keys_str_mv | AT stevensonpm renormalizedperturbationtheoryanditsoptimizationbytheprincipleofminimalsensitivity |