Renormalization Group / / Giuseppe Benfatto, Giovanni Gallavotti.
Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics...
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Benfatto, Giuseppe, author. aut http://id.loc.gov/vocabulary/relators/aut Renormalization Group / Giuseppe Benfatto, Giovanni Gallavotti. Princeton, NJ : Princeton University Press, [2020] ©1995 1 online resource (140 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Physics Notes ; 1 Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- Chapter 2. Problems Equivalent to the Analysis of Suitable Functional Integrals: Critical Point and Field Theory -- Chapter 3. Other Functional Integrals: Fermi Sphere and Bose Condensation -- Chapter 4. Effective Potentials and Schwinger Functions -- Chapter 5. Multiscale Decomposition of Propagators and Fields: Running Effective Potentials -- Chapter 6. Renormalization Group: Relevant and Irrelevant Components of the Effective Potentials -- Chapter 7. Asymptotic Freedom: Upper Critical Dimension -- Chapter 8. Beyond the Linear Approximations: The Beta Function and Perturbation The -- Chapter 9. The Beta Function as a Dynamical System: Asymptotic Freedom of Marginal Theories -- Chapter 10. Anomalous Dimension -- Chapter 11. The Fermi Liquid and the Luttinger Model -- Chapter 12. The Generic Critical Point for d = 3,7 = 0: The ^-Expansion -- Chapter 13. Bose Condensation: Reformulation -- Chapter 14. Bose Condensation: Effective Potentials -- Chapter 15. The Beta Function for the Bose Conden -- A Brief Historical Note -- Bibliographical Notes -- Appendix 1. The Free Fermion Propagator -- Appendix 2. Grassmannian Integration -- Appendix 3. Trees and Feynman Graphs -- Appendix 4. Schwinger Functions and Anomalous Dimension -- Appendix 5. Propagators for the Bose Gas -- Appendix 6. The Beta Function for the Bose Gas -- References -- Subject Index -- Citation Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems. The dimension dependence is discussed together with the related existence of anomalies (in Tomonaga's theory and in 4 -e dimensions for the critical point). The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention is focused on results that can in principle be formally established from a mathematical point of view. The 4 -e dimensions theory, Bose condensation, as well as a few other statements are exceptions to this rule, because no complete treatment is yet available. However, the truly mathematical details are intentionally omitted and only referred to. This is done with the purpose of stressing the unifying conceptual structure rather than the technical differences or subtleties. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Critical phenomena (Physics). Renormalization group. SCIENCE / Physics / General. bisacsh Anomalous dimension. Asymptotic freedom. Beta function. Bose condensation. Chemical potential. Critical point. Dimensional potential. Euclidean field. Fermi liquid. Feynman graph. Gaussian measure. Generating functional. Grassmannian variable. Hadamard inequality. Infrared problem. Irrelevant part. Kernel. Landau-Ginsburg model. Localization operator. Marginal operator. Normal critical behavior. Propagator matrix. Propagator. Renormalizable theory. Schwinger function. Superfluid behavior. Tree formalism. Ultraviolet problem. Wick monomial. Gallavotti, Giovanni, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 https://doi.org/10.1515/9780691221694?locatt=mode:legacy https://www.degruyter.com/isbn/9780691221694 Cover https://www.degruyter.com/cover/covers/9780691221694.jpg |
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author |
Benfatto, Giuseppe, Benfatto, Giuseppe, Gallavotti, Giovanni, |
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Benfatto, Giuseppe, Benfatto, Giuseppe, Gallavotti, Giovanni, Renormalization Group / Physics Notes ; Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- Chapter 2. Problems Equivalent to the Analysis of Suitable Functional Integrals: Critical Point and Field Theory -- Chapter 3. Other Functional Integrals: Fermi Sphere and Bose Condensation -- Chapter 4. Effective Potentials and Schwinger Functions -- Chapter 5. Multiscale Decomposition of Propagators and Fields: Running Effective Potentials -- Chapter 6. Renormalization Group: Relevant and Irrelevant Components of the Effective Potentials -- Chapter 7. Asymptotic Freedom: Upper Critical Dimension -- Chapter 8. Beyond the Linear Approximations: The Beta Function and Perturbation The -- Chapter 9. The Beta Function as a Dynamical System: Asymptotic Freedom of Marginal Theories -- Chapter 10. Anomalous Dimension -- Chapter 11. The Fermi Liquid and the Luttinger Model -- Chapter 12. The Generic Critical Point for d = 3,7 = 0: The ^-Expansion -- Chapter 13. Bose Condensation: Reformulation -- Chapter 14. Bose Condensation: Effective Potentials -- Chapter 15. The Beta Function for the Bose Conden -- A Brief Historical Note -- Bibliographical Notes -- Appendix 1. The Free Fermion Propagator -- Appendix 2. Grassmannian Integration -- Appendix 3. Trees and Feynman Graphs -- Appendix 4. Schwinger Functions and Anomalous Dimension -- Appendix 5. Propagators for the Bose Gas -- Appendix 6. The Beta Function for the Bose Gas -- References -- Subject Index -- Citation Index |
author_facet |
Benfatto, Giuseppe, Benfatto, Giuseppe, Gallavotti, Giovanni, Gallavotti, Giovanni, Gallavotti, Giovanni, |
author_variant |
g b gb g b gb g g gg |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Gallavotti, Giovanni, Gallavotti, Giovanni, |
author2_variant |
g g gg |
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VerfasserIn VerfasserIn |
author_sort |
Benfatto, Giuseppe, |
title |
Renormalization Group / |
title_full |
Renormalization Group / Giuseppe Benfatto, Giovanni Gallavotti. |
title_fullStr |
Renormalization Group / Giuseppe Benfatto, Giovanni Gallavotti. |
title_full_unstemmed |
Renormalization Group / Giuseppe Benfatto, Giovanni Gallavotti. |
title_auth |
Renormalization Group / |
title_alt |
Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- Chapter 2. Problems Equivalent to the Analysis of Suitable Functional Integrals: Critical Point and Field Theory -- Chapter 3. Other Functional Integrals: Fermi Sphere and Bose Condensation -- Chapter 4. Effective Potentials and Schwinger Functions -- Chapter 5. Multiscale Decomposition of Propagators and Fields: Running Effective Potentials -- Chapter 6. Renormalization Group: Relevant and Irrelevant Components of the Effective Potentials -- Chapter 7. Asymptotic Freedom: Upper Critical Dimension -- Chapter 8. Beyond the Linear Approximations: The Beta Function and Perturbation The -- Chapter 9. The Beta Function as a Dynamical System: Asymptotic Freedom of Marginal Theories -- Chapter 10. Anomalous Dimension -- Chapter 11. The Fermi Liquid and the Luttinger Model -- Chapter 12. The Generic Critical Point for d = 3,7 = 0: The ^-Expansion -- Chapter 13. Bose Condensation: Reformulation -- Chapter 14. Bose Condensation: Effective Potentials -- Chapter 15. The Beta Function for the Bose Conden -- A Brief Historical Note -- Bibliographical Notes -- Appendix 1. The Free Fermion Propagator -- Appendix 2. Grassmannian Integration -- Appendix 3. Trees and Feynman Graphs -- Appendix 4. Schwinger Functions and Anomalous Dimension -- Appendix 5. Propagators for the Bose Gas -- Appendix 6. The Beta Function for the Bose Gas -- References -- Subject Index -- Citation Index |
title_new |
Renormalization Group / |
title_sort |
renormalization group / |
series |
Physics Notes ; |
series2 |
Physics Notes ; |
publisher |
Princeton University Press, |
publishDate |
2020 |
physical |
1 online resource (140 p.) |
contents |
Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- Chapter 2. Problems Equivalent to the Analysis of Suitable Functional Integrals: Critical Point and Field Theory -- Chapter 3. Other Functional Integrals: Fermi Sphere and Bose Condensation -- Chapter 4. Effective Potentials and Schwinger Functions -- Chapter 5. Multiscale Decomposition of Propagators and Fields: Running Effective Potentials -- Chapter 6. Renormalization Group: Relevant and Irrelevant Components of the Effective Potentials -- Chapter 7. Asymptotic Freedom: Upper Critical Dimension -- Chapter 8. Beyond the Linear Approximations: The Beta Function and Perturbation The -- Chapter 9. The Beta Function as a Dynamical System: Asymptotic Freedom of Marginal Theories -- Chapter 10. Anomalous Dimension -- Chapter 11. The Fermi Liquid and the Luttinger Model -- Chapter 12. The Generic Critical Point for d = 3,7 = 0: The ^-Expansion -- Chapter 13. Bose Condensation: Reformulation -- Chapter 14. Bose Condensation: Effective Potentials -- Chapter 15. The Beta Function for the Bose Conden -- A Brief Historical Note -- Bibliographical Notes -- Appendix 1. The Free Fermion Propagator -- Appendix 2. Grassmannian Integration -- Appendix 3. Trees and Feynman Graphs -- Appendix 4. Schwinger Functions and Anomalous Dimension -- Appendix 5. Propagators for the Bose Gas -- Appendix 6. The Beta Function for the Bose Gas -- References -- Subject Index -- Citation Index |
isbn |
9780691221694 9783110442496 |
url |
https://doi.org/10.1515/9780691221694?locatt=mode:legacy https://www.degruyter.com/isbn/9780691221694 https://www.degruyter.com/cover/covers/9780691221694.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
530 - Physics |
dewey-ones |
530 - Physics |
dewey-full |
530.1/33 |
dewey-sort |
3530.1 233 |
dewey-raw |
530.1/33 |
dewey-search |
530.1/33 |
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10.1515/9780691221694?locatt=mode:legacy |
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1229160789 |
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Renormalization Group / |
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