Horatiu NastaseCambridge University Press, 10/17/2019EAN 9781108493994, ISBN10: 1108493998Hardcover, 730 pages, 25.4 x 19.6 x 3.8 cmLanguage: EnglishQuantum Field Theory provides a theoretical framework for understanding fields and the particles associated with them, and is the basis of particle physics and condensed matter research. This graduate level textbook provides a comprehensive introduction to quantum field theory, giving equal emphasis to operator and path integral formalisms. It covers modern research such as helicity spinors, BCFW construction and generalized unitarity cuts; as well as treating advanced topics including BRST quantization, loop equations, and finite temperature field theory. Various quantum fields are described, including scalar and fermionic fields, Abelian vector fields and Quantum ElectroDynamics (QED), and finally non-Abelian vector fields and Quantum ChromoDynamics (QCD). Applications to scattering cross sections in QED and QCD are also described. Each chapter ends with exercises and an important concepts section, allowing students to identify the key aspects of the chapter and test their understanding.1. Review of classical field theory2. Quantum mechanics3. Canonical quantization of scalar fields4. Propagators for free scalar fields5. Interaction picture and wick theorem for ΛÆ4 in operator formalism6. Feynman rules for ΛÆ4 from the operator formalism7. The driven (forced) harmonic oscillator8. Euclidean formulation and finite temperature field theory9. The Feynman path integral for a scalar field10. Wick theorem for path integrals and Feynman rules part I11. Feynman rules in X-Space and P-Space12. Quantization of the Dirac field and Fermionic path integral13. Wick theorem, Gaussian integration and Feynman rules for fermions14. Spin sums, Dirac field bilinears and C,P,T symmetries for fermions15. Dirac quantization of constrained systems16. Quantization of gauge fields, their path integral, and the photon propagator17. Generating functional for connected Green's Functions and the effective action (1PI Diagrams)18. Dyson–Schwinger equations and ward identities19. Cross sections and the S-Matrix20. The S-matrix and Feynman diagrams21. The optical theorem and the cutting rules22. Unitarity and the largest time equation23. QED24. Nonrelativistic processes25. E+E− → L¯ L unpolarized cross section26. E+E− →L¯ L polarized cross section27. (Unpolarized) Compton scattering28. The Helicity Spinor formalism29. Gluon amplitudes, the Parke–Taylor formula and the BCFW construction30. Review of path integral and operator formalism and the Feynman diagram expansion31. One-loop determinants, vacuum energy and zeta function regularization32. One-loop divergences for scalars33. Regularization, definitions34. One-loop renormalization for scalars and counterterms in dimensional regularization35. Renormalization conditions and the renormalization group36. One-loop renormalizability in QED37. Physical applications of one-loop results 1. Vacuum Polarization38. Physical applications of one-loop results 2. Anomalous magnetic moment and lamb shift39. Two-loop example and multiloop generalization40. The LSZ reduction formula41. The Coleman–Weinberg mechanism for one-loop potential42. Quantization of gauge theories I43. Quantization of gauge theories II44. One-loop renormalizability of gauge theories45. Asymptotic freedom. BRST symmetry46. Lee–Zinn–Justin identities and the structure of divergences (formal renormalization of gauge theories)47. BRST quantization48. QCD49. Parton evolution and Altarelli-Parisi equation50. The Wilson Loop and the Makeenko–Migdal Loop equation. Order parameters'T Hooft Loop51. IR divergences in QED52. IR safety and renormalization in QCDGeneral IR-factorized form of amplitudes53. Factorization and the Kinoshita–Lee–Nauenberg theorem54. Perturbatives anomalies55. Anomalies in path integrals – the Fujikawa method56. Physical applications of anomalies, 'T Hooft's UV-IR anomaly matching conditions, anomaly cancellation57. The Froissart Unitarity Bound and the Heisenberg Model58. The operator product expansion, renormalization of composite operators and anomalous dimension matrices59. Manipulating loop amplitudes60. Analyzing the result for amplitudes61. Representations and symmetries for loop amplitudes62. The Wilsonian effective action, effective field theory and applications63. Kadanoff blocking and the renormalization group64. Lattice field theory65. The Higgs Mechanism66. Renormalization of spontaneously broken gauge theories I67. Renormalization of spontaneously broken gauge theories II68. Pseudo-Goldstone bosons, nonlinear sigma model and Chiral perturbation theory69. The background field method70. Finite temperature quantum field theory I71. Finite temperature quantum field theory II72. Finite temperature quantum field theory III.
