Renormalization Group:
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...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2020]
|
| Schriftenreihe: | Physics Notes
1 |
| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 UPA01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 06. Jan 2021) |
| Beschreibung: | 1 online resource |
| ISBN: | 9780691221694 |
| DOI: | 10.1515/9780691221694 |
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| 520 | |a 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 | ||
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| 650 | 4 | |a Critical point | |
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| spelling | Benfatto, Giuseppe Verfasser aut Renormalization Group Giovanni Gallavotti, Giuseppe Benfatto Princeton, NJ Princeton University Press [2020] © 1995 1 online resource txt rdacontent c rdamedia cr rdacarrier Physics Notes 1 Description based on online resource; title from PDF title page (publisher's Web site, viewed 06. Jan 2021) 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 In English 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 Renormalization group Schwinger function Superfluid behavior Tree formalism Ultraviolet problem Wick monomial SCIENCE / Physics / General bisacsh Critical phenomena (Physics) Gallavotti, Giovanni aut https://doi.org/10.1515/9780691221694 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Benfatto, Giuseppe Gallavotti, Giovanni Renormalization Group 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 Renormalization group Schwinger function Superfluid behavior Tree formalism Ultraviolet problem Wick monomial SCIENCE / Physics / General bisacsh Critical phenomena (Physics) |
| title | Renormalization Group |
| title_auth | Renormalization Group |
| title_exact_search | Renormalization Group |
| title_exact_search_txtP | Renormalization Group |
| title_full | Renormalization Group Giovanni Gallavotti, Giuseppe Benfatto |
| title_fullStr | Renormalization Group Giovanni Gallavotti, Giuseppe Benfatto |
| title_full_unstemmed | Renormalization Group Giovanni Gallavotti, Giuseppe Benfatto |
| title_short | Renormalization Group |
| title_sort | renormalization group |
| topic | 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 Renormalization group Schwinger function Superfluid behavior Tree formalism Ultraviolet problem Wick monomial SCIENCE / Physics / General bisacsh Critical phenomena (Physics) |
| topic_facet | 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 Renormalization group Schwinger function Superfluid behavior Tree formalism Ultraviolet problem Wick monomial SCIENCE / Physics / General Critical phenomena (Physics) |
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