Introduction to Quantum Field Theory
Cambridge University Press, 10/17/2019
EAN 9781108493994, ISBN10: 1108493998
Hardcover, 730 pages, 25.4 x 19.6 x 3.8 cm
Language: English
Quantum 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 theory
2. Quantum mechanics
3. Canonical quantization of scalar fields
4. Propagators for free scalar fields
5. Interaction picture and wick theorem for ΛÆ4 in operator formalism
6. Feynman rules for ΛÆ4 from the operator formalism
7. The driven (forced) harmonic oscillator
8. Euclidean formulation and finite temperature field theory
9. The Feynman path integral for a scalar field
10. Wick theorem for path integrals and Feynman rules part I
11. Feynman rules in X-Space and P-Space
12. Quantization of the Dirac field and Fermionic path integral
13. Wick theorem, Gaussian integration and Feynman rules for fermions
14. Spin sums, Dirac field bilinears and C,P,T symmetries for fermions
15. Dirac quantization of constrained systems
16. Quantization of gauge fields, their path integral, and the photon propagator
17. Generating functional for connected Green's Functions and the effective action (1PI Diagrams)
18. Dyson–Schwinger equations and ward identities
19. Cross sections and the S-Matrix
20. The S-matrix and Feynman diagrams
21. The optical theorem and the cutting rules
22. Unitarity and the largest time equation
23. QED
24. Nonrelativistic processes
25. E+E− → L¯ L unpolarized cross section
26. E+E− →L¯ L polarized cross section
27. (Unpolarized) Compton scattering
28. The Helicity Spinor formalism
29. Gluon amplitudes, the Parke–Taylor formula and the BCFW construction
30. Review of path integral and operator formalism and the Feynman diagram expansion
31. One-loop determinants, vacuum energy and zeta function regularization
32. One-loop divergences for scalars
33. Regularization, definitions
34. One-loop renormalization for scalars and counterterms in dimensional regularization
35. Renormalization conditions and the renormalization group
36. One-loop renormalizability in QED
37. Physical applications of one-loop results 1. Vacuum Polarization
38. Physical applications of one-loop results 2. Anomalous magnetic moment and lamb shift
39. Two-loop example and multiloop generalization
40. The LSZ reduction formula
41. The Coleman–Weinberg mechanism for one-loop potential
42. Quantization of gauge theories I
43. Quantization of gauge theories II
44. One-loop renormalizability of gauge theories
45. Asymptotic freedom. BRST symmetry
46. Lee–Zinn–Justin identities and the structure of divergences (formal renormalization of gauge theories)
47. BRST quantization
48. QCD
49. Parton evolution and Altarelli-Parisi equation
50. The Wilson Loop and the Makeenko–Migdal Loop equation. Order parameters
'T Hooft Loop
51. IR divergences in QED
52. IR safety and renormalization in QCD
General IR-factorized form of amplitudes
53. Factorization and the Kinoshita–Lee–Nauenberg theorem
54. Perturbatives anomalies
55. Anomalies in path integrals – the Fujikawa method
56. Physical applications of anomalies, 'T Hooft's UV-IR anomaly matching conditions, anomaly cancellation
57. The Froissart Unitarity Bound and the Heisenberg Model
58. The operator product expansion, renormalization of composite operators and anomalous dimension matrices
59. Manipulating loop amplitudes
60. Analyzing the result for amplitudes
61. Representations and symmetries for loop amplitudes
62. The Wilsonian effective action, effective field theory and applications
63. Kadanoff blocking and the renormalization group
64. Lattice field theory
65. The Higgs Mechanism
66. Renormalization of spontaneously broken gauge theories I
67. Renormalization of spontaneously broken gauge theories II
68. Pseudo-Goldstone bosons, nonlinear sigma model and Chiral perturbation theory
69. The background field method
70. Finite temperature quantum field theory I
71. Finite temperature quantum field theory II
72. Finite temperature quantum field theory III.