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Viser: Quantum Field Theory and Critical Phenomena - Fifth Edition
Quantum Field Theory and Critical Phenomena
Fifth Edition
Jean Zinn-Justin
(2026)
Sprog: Engelsk
Oxford University Press, Incorporated
738,00 kr.
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Detaljer om varen
- 5. Udgave
- Paperback: 1088 sider
- Udgiver: Oxford University Press, Incorporated (Marts 2026)
- ISBN: 9780198994893
Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamics has been the first example of a Quantum Field Theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics. As this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale. Therefore, this text sets out to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group properties are systematically discussed. The notion of effective field theory and the emergence of renormalisable theories are described. The consequences for fine tuning and triviality issue are emphasized. This fifth edition has been updated and fully revised, e.g. in particle physics with progress in neutrino physics and the discovery of the Higgs boson. The presentation has been made more homogeneous througout the volume, and emphasis has been put on the notion of effective field theory and discussion of the emergence of renormalisable theories.
Preface1. Gaussian integrals. Algebraic preliminaries2. Euclidean path integrals and quantum mechanics3. Quantum mechanics: Path integrals in phase space4. Quantum statistical physics: Functional integration formalism5. Quantum evolution: From particles to fields6. The neutral relativistic scalar field7. Perturbative quantum field theory: Algebraic methods8. Ultraviolet divergences: Effective quantum field theory9. Introduction to renormalization theory and renormalization group10. Dimensional continuation, regularization. Minimal subtraction, RG functions11. Renormalization of local polynomials. Short distance expansion12. Relativistic fermions: Introduction13. Symmetries, chiral symmetry breaking and renormalization14. Critical phenomena: General considerations. Mean-field theory15. The renormalization group approach: The critical theory near dimension
416. Critical domain: Universality, "-expansion17. Critical phenomena: Corrections to scaling behaviour18. O(N)-symmetric vector models for N large19. The non-linear ?-model near two dimensions: Phase structure20. Gross-Neveu-Yukawa and Gross-Neveu models21. Abelian gauge theories: The framework of quantum electrodynamics22. Non-Abelian gauge theories: Introduction23. The Standard Model of fundamental interactions24. Large momentum behaviour in quantum field theory25. Lattice gauge theories: Introduction26. BRST symmetry, gauge theories: Zinn-Justin equation and renormalization27. Supersymmetric quantum field theory: Introduction28. Elements of classical and quantum gravity29. Generalized non-linear ?-models in two dimensions30. A few two-dimensional solvable quantum field theories31. O(2) spin model and Kosterlitz-Thouless's phase transition32. Finite-size effects in field theory. Scaling behaviour33. Quantum field theory at finite temperature: Equilibrium properties34. Stochastic differential equations: Langevin, Fokker-Planck equations35. Langevin field equations, properties and renormalization36. Critical dynamics and renormalization group37. Instantons in quantum mechanics38. Metastable vacua in quantum field theory39. Degenerate classical minima and instantons40. Perturbative expansion at large orders41. Critical exponents and equation of state from series summation42. Multi-instantons in quantum mechanicsBibliographyIndex
416. Critical domain: Universality, "-expansion17. Critical phenomena: Corrections to scaling behaviour18. O(N)-symmetric vector models for N large19. The non-linear ?-model near two dimensions: Phase structure20. Gross-Neveu-Yukawa and Gross-Neveu models21. Abelian gauge theories: The framework of quantum electrodynamics22. Non-Abelian gauge theories: Introduction23. The Standard Model of fundamental interactions24. Large momentum behaviour in quantum field theory25. Lattice gauge theories: Introduction26. BRST symmetry, gauge theories: Zinn-Justin equation and renormalization27. Supersymmetric quantum field theory: Introduction28. Elements of classical and quantum gravity29. Generalized non-linear ?-models in two dimensions30. A few two-dimensional solvable quantum field theories31. O(2) spin model and Kosterlitz-Thouless's phase transition32. Finite-size effects in field theory. Scaling behaviour33. Quantum field theory at finite temperature: Equilibrium properties34. Stochastic differential equations: Langevin, Fokker-Planck equations35. Langevin field equations, properties and renormalization36. Critical dynamics and renormalization group37. Instantons in quantum mechanics38. Metastable vacua in quantum field theory39. Degenerate classical minima and instantons40. Perturbative expansion at large orders41. Critical exponents and equation of state from series summation42. Multi-instantons in quantum mechanicsBibliographyIndex
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