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Critical properties of [Greek letter phi]4-theories /
This work explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
River Edge, N.J. :
World Scientific,
©2001.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Introduction. 1.1. Second-order phase transitions. 1.2. Critical exponents. 1.3. Models for critical behavior. 1.4. Fluctuating fields. 1.5. General remarks
- 2. Definition of [symbol]-theory. 2.1. Partition function and generating functional. 2.2. Free-field theory. 2.3. Perturbation expansion. 2.4. Composite fields
- 3. Feynman diagrams. 3.1. Diagrammatic expansion of correlation functions. 3.2. Diagrammatic expansion of the partition function. 3.3. Connected and disconnected diagrams. 3.4. Connected diagrams for two- and four-point functions. 3.5. Diagrams for composite fields
- 4. Diagrams in momentum space. 4.1. Fourier transformation. 4.2. One-particle irreducible diagrams and proper vertex functions. 4.3. Composite fields. 4.4. Theory in continuous dimension D
- 5. Structural properties of perturbation theory. 5.1. Generating functionals. 5.2. Connectedness structure of correlation functions. 5.3. Decomposition of correlation functions into connected correlation functions. 5.4. Functional generation of vacuum diagrams. 5.5. Correlation functions from vacuum diagrams. 5.6. Generating functional for vertex functions. 5.7. Landau approximation to generating functional. 5.8. Composite fields
- 6. Diagrams for multicomponent fields. 6.1. Interactions with O(N) cubic symmetry. 6.2. Free generating functional for N fields. 6.3. Perturbation expansion for TV fields and symmetry factors. 6.4. Symmetry factors
- 7. Scale transformations of fields and correlation functions. 7.1. Free massless fields. 7.2. Free massive fields. 7.3. Interacting fields. 7.4. Anomaly in the ward identities
- 8. Regularization of Feynman integrals. 8.1. Regularization. 8.2. Dimensional regularization. 8.3. Calculation of one-particle-irreducible diagrams
- 9. Renormalization. 9.1. Superficial degree of divergence. 9.2. Normalization conditions. 9.3. Method of counterterms and minimal subtraction
- 10. Renormalization group. 10.1. Callan-Symanzik equation. 10.2. Renormalization group equation. 10.3. Calculation of coefficient functions from counterterms. 10.4. Solution of the renormalization group equation. 10.5. Fixed point. 10.6. Effective energy and potential. 10.7. Special properties of ground state energy. 10.8. Approach to scaling. 10.9. Further critical exponents. 10.10. Scaling relations below Tc. 10.11. Comparison of scaling relations with experiment. 10.12. Critical values g*, n, v, and w in powers of e. 10.13. Several coupling constants. 10.14. Ultraviolet versus infrared properties
- 11. Recursive subtraction of UV-divergences by R-operation. 11.1. Graph-theoretic notations. 11.2. Definition of R- and R-operation. 11.3. Properties of diagrams with cutvertices. 11.4. Tadpoles in diagrams with superficial logarithmic divergence. 11.5. Nontrivial example for R-operation. 11.6. Counterterms in minimal subtraction. 11.7. Simplifications for Zm2. 11.8. Simplifications for Z[symbol]
- 12. Zero-mass approach to counterterms. 12.1. Infrared power counting. 12.2. Infrared rearrangement. 12.3. Infrared divergences in dimensional regularization. 12.4. Subtraction of UV- and IR-divergences: R*-operation. 12.5. Examples for the R*-operation
- 13. Calculation of momentum space integrals. 13.1. Simple loop integrals. 13.2. Classification of diagrams. 13.3. Five-loop diagrams. 13.4. Reduction algorithm based on partial integration. 13.5. Method of ideal index constellations in configuration space. 13.6. Special treatment of Generic four- and five-loop diagrams. 13.7. Computer-algebraic program
- 14. Generation of diagrams. 14.1. Algebraic representation of diagrams. 14.2. Generation procedure
- 15. Results of the five-loop calculation. 15.1. Renormalization constants for O(N)-symmetric theory. 15.2. Renormalization constants for theory with mixed O(N) and cubic-symmetry. 15.3. Renormalization constant for vacuum energy
- 16. Basic resummation theory. 16.1. Asymptotic series. 16.2. Pade approximants. 16.3. Borel transformation. 16.4. Conformal mappings. 16.5. Janke-Kleinert resummation algorithm. 16.6. Modified reexpansions
- 17. Critical exponents of O(N)-symmetric theory. 17.1. Series expansions for renormalization group functions. 17.2. Fixed point and critical exponents. 17.3. Large-order behavior. 17.4. Resummation
- 18. Cubic anisotropy. 18.1. Basic properties. 18.2. Series expansions for RG functions. 18.3. Fixed points and critical exponents. 18.4. Stability. 18.5. Resummation
- 19. Variational perturbation theory. 19.1. From weak- to strong-coupling expansions. 19.2. Strong-coupling theory. 19.3. Convergence. 19.4. Strong-coupling limit and critical exponents. 19.5. Explicit low-order calculations. 19.6. Three-loop resummation. 19.7. Five-loop resummation. 19.8. Interpolating critical exponents between two and four dimensions
- 20. Critical exponents from other expansions. 20.1. Sixth-order expansion in three dimensions. 20.2. Critical exponents up to six loops. 20.3. Improving the graphical extrapolation of critical exponents. 20.4. Seven-loop results for N = 0, 1, 2, and 3. 20.5. Large-order behavior. 20.6. Influence of large-order information. 20.7. Another variational resummation method. 20.8. High-temperature expansions of lattice models
- 21. New resummation algorithm. 21.1. Hyper-borel transformation. 21.2. Convergence properties. 21.3. Resummation of ground state energy of anharmonic oscillator. 21.4. Resummation for critical exponents.