经典场论 Classical Field Theory 英文原版 Horatiu Nastase

基本信息

Format Hardback | 480 pages

Dimensions 192 x 253 x 26mm | 1,200g

Publication date 30 Apr 2019

Publisher Cambridge University Press

Language English

Illustrations note Worked examples or Exercises; 3 Halftones, black and white; 34 Line drawings, black and white

ISBN10 1108477011

ISBN13 9781108477017

页面参数仅供参考，具体以实物为准

书籍简介

《经典场论》预测物理场如何与物质相互作用，是量子场论的逻辑先驱。 本介绍纯粹关注现代经典场论，帮助毕业生和研究人员在开始量子场论的未来研究之前建立对经典场论方法的理解。 它描述了具有可忽略量子效应的场的各种经典方法，例如电磁场和引力场。 它侧重于利用经典场论方法而不是应用程序或几何特性的解决方案。 涵盖的其他领域包括费米子场、标量场和陈-西蒙斯场。 还讨论了对称性、全局和局部方法、诺特定理和能量动量张量等方法，以及经典方程的重要解，特别是孤子解。

Classical field theory predicts how physical fields interact with matter, and is a logical precursor to quantum field theory. This introduction focuses purely on modern classical field theory, helping graduates and researchers build an understanding of classical field theory methods before embarking on future studies in quantum field theory. It describes various classical methods for fields with negligible quantum effects, for instance electromagnetism and gravitational fields. It focuses on solutions that take advantage of classical field theory methods as opposed to applications or geometric properties. Other fields covered includes fermionic fields, scalar fields and Chern-Simons fields. Methods such as symmetries, global and local methods, Noether theorem and energy momentum tensor are also discussed, as well as important solutions of the classical equations, in particular soliton solutions.

目录

Preface; Introduction; 1. Short review of classical mechanics; 2. Symmetries, groups and Lie algebras. Representations; 3. Examples: the rotation group and SU(2); 4. Review of special relativity. Lorentz tensors; 5. Lagrangeans and the notion of field; electromagnetism as a field theory; 6. Scalar field theory, origins and applications; 7. Nonrelativistic examples; water waves, surface growth; 8. Classical integrability. Continuum limit of discrete, lattice and spin systems; 9. Poisson brackets for field theory and equations of motion. Applications; 10. Classical perturbation theory and formal solutions to the equations of motion; 11. Representations of the Lorentz group; 12. Statistics, symmetry, and the spin-statistics theorem; 13. Electromagnetism and the Maxwell equation; Abelian vector fields; Proca field; 14. The energy-momentum tensor; 15. Motion of charged particles and electromagnetic waves; Maxwell duality; 16. The Hopfion solution and the Hopf map; 17. Complex scalar field and electric current. Gauging a global symmetry; 18. The Noether theorem and applications; 19. Nonrelativistic and relativistic fluid dynamics. Fluid vortices and knots; 20. Kink solutions in o4 and sine-Gordon, domain walls and topology; 21. The Skyrmion scalar field solution and topology; 22. Field theory solitons for condensed matter: the XY and rotor model, spins, superconductivity and the KT transition; 23. Radiation of a classical scalar field. The Heisenberg model; 24. Derrick's theorem, Bogomolnyi bound, the Abelian-Higgs system and symmetry breaking; 25. The Nielsen-Olesen vortex, topology and applications; 26. Nonabelian gauge theory and the Yang-Mills equation; 27. The Dirac monopole and Dirac quantization; 28. The 't Hooft-Polyakov monopole solution and topology; 29. The BPST-'t Hooft instanton solution and topology; 30. General topology and reduction on an ansatz; 31. Other soliton types. Nontopological solitons: Q-balls; unstable solitons: sphalerons; 32. Moduli space; soliton scattering in moduli space approximation; collective coordinates; 33. Chern-Simons terms: emergent gauge fields, the Quantum Hall Effect (integer and fractional), anyonic statistics; 34. Chern-Simons and self-duality in odd dimensions, its duality to topologically massive theory and dualities in general; 35. Particle-vortex duality in 3 dimensions, particle-string duality in 4 dimensions, and p-form fields in 4 dimensions; 36. Fermions and Dirac spinors; 37. The Dirac equation at its solutions; 38. General relativity: metric and general coordinate invariance; 39. The Einstein action and the Einstein equation; 40. Perturbative gravity: Fierz-Pauli action, de Donder gauge and other gauges, gravitational waves; 41. Nonperturbative gravity: the vacuum Schwarzschild solution; 42. Deflection of light by the Sun and comparison with general relativity; 43. Fully linear gravity: parallel plane (pp) waves and gravitational shockwave solutions; 44. Dimensional reduction: the domain wall, cosmic string and BTZ black hole solutions; 45. Time dependent gravity: the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological solution; 46. Vielbein-spin connection formulation of general relativity and gravitational instantons; References; Index.

作者简介

Horatiu Nastase 是圣保罗大学保利斯塔大学理论物理研究所的研究员。 迄今为止，他的职业生涯已跨越四大洲。 作为一名本科生，他曾就读于布加勒斯特大学和科本港大学。 他后来完成了博士学位。 在搬到新泽西州普林斯顿大学高级研究所之前，他在纽约州立大学石溪分校与 David Berenstein 和 Juan Maldacena 合作定义了 pp 波对应。 他还曾在罗德岛布朗大学和东京工业大学担任研究和教学职位。

Horatiu Nastase is a Researcher at the Institute for Theoretical Physics at the Universidade Estadual Paulista, Sao Paulo. To date, his career has spanned four continents. As an undergraduate he studied at the Universitatea din Bucuresti and Kobenhavns Universitet. He later completed his Ph.D. at the State University of New York, Stony Brook, before moving to the Institute for Advanced Study, Princeton University, New Jersey, where his collaboration with David Berenstein and Juan Maldacena defined the pp-wave correspondence. He has also held research and teaching positions at Brown University, Rhode Island and the Tokyo Institute of Technology.