Regular Courses at IFT (Portuguese and English)

Quantum Field Theory II - 1st Semester, 2022

  • Credits: 12 (in "hours per week")
    Prerequisites: Quantum Field Theory I
    Meetings: twice a week (according to this schedule)
  • Overview:
    The course will be offered jointly by Profs. Ricardo Matheus and Horatiu Nastase. We will go through the syllabus below following ref [1]. It is assumed that students have already studied (relativistic) Quantum Field Theories, and only a very limited review of them will be offered.

    Grades will be based on exercises.
  • Syllabus, video lectures and meetings:
    The lectures will be on YouTube, and the students are expected to watch them and work through the exercises. Twice a week there will be a meeting in which the students are expected to discuss the lecture and exercises. These meetings will be attended by one of the two professors offering the course, as indicated in the following list.

    Below are the links to the video-lectures, the corresponding chapter in ref [1] and the professor assigned to the meeting. For the full playlist go here.

    • Lecture 1 (Chapter 32. One-loop divergences, renormalizability and power counting) - prof. Ricardo Matheus (March 9)
    • Lecture 2 (Chapter 33. Regularization, definitions: cut-off, Pauli-Villars, dimensional regularization, general Feynman parametrization) - prof. Ricardo Matheus (March 14)
    • Lecture 3 (Chapter 34. One-loop renormalization for scalars and counterterms in dimensional regularization) - prof. Ricardo Matheus (March 16)
    • Lecture 4 (Chapter 35. Renormalization conditions and the renormalization group) - prof. Ricardo Matheus (March 21)
    • Lecture 5 (Chapter 36. One-loop renormalizability in QED) - prof. Ricardo Matheus (March 23)
    • Lecture 6* (Chapter 37. Physical applications of one-loop results 1. Vacuum polarization) - prof. Horatiu Nastase (March 28)
    • Lecture 7 (Chapter 38. Physical applications of one-loop results 2. Anomalous magnetic moment and Lamb shift) - prof. Horatiu Nastase (March 30)
    • Lecture 8 (Chapter 39. Two-loop example and multiloop generalization) - prof. Horatiu Nastase (April 4)
    • Lecture 9 (Chapter 40. The LSZ formula) - prof. Ricardo Matheus (April 6)
    • Lecture 10 (Chapter 42. Quantization of gauge theories I: path integrals and Fadeev-Popov) - prof. Ricardo Matheus (April 11)
    • Lecture 11 (Chapter 43. Quantization of gauge theories 2. Propagators and Feynman rules) - prof. Ricardo Matheus (April 13)
    • Lecture 12 (Chapter 44. One-loop renormalizability of gauge theories) - prof. Horatiu Nastase (April 18)
    • Lecture 13 (Chapter 45. Asymptotic freedom. BRST symmetry) - prof. Horatiu Nastase (April 20)
    • Lecture 14 (Chapter 46. Lee-Zinn-Justin identities and the structure of divergences) - prof. Horatiu Nastase (April 25)
    • Lecture 15 (Chapter 47. BRST quantization) - prof. Horatiu Nastase (April 27)
    • Lecture 16 (Chapter 48. QCD: definition, deep inelastic scattering) - prof. Ricardo Matheus (May 2)
    • Lecture 17 (Chapter 49. Parton evolution and Altarelli-Parisi equation) - prof. Ricardo Matheus (May 4)
    • Lecture 18 (Chapter 50. The Wilson loop and the Makeenko-Migdal loop equation. Order parameters; 't Hooft loop) - prof. Horatiu Nastase (May 9)
    • Lecture 19 (Chapter 51. IR divergences in QED) - prof. Ricardo Matheus (May 11)
    • Lecture 20 (Chapter 52. IR safety and renormalization in QCD; general IR-factorized form of amplitudes) - prof. Ricardo Matheus (May 16)
    • Lecture 21 (Chapter 53. Factorization and the Kinoshita-Lee-Nauenberg theorem) - prof. Horatiu Nastase (May 18)
    • Lecture 22 (Chapter 54. Perturbatives anomalies: chiral and gauge) - prof. Horatiu Nastase (May 23)
    • Lecture 23 (Chapter 55. Anomalies in path integrals- the Fujikawa method; consistent vs. covariant anomalies and descent equations) - prof. Horatiu Nastase (May 25)
    • Lecture 24 (Chapter 56. Physical applications of anomalies: 't Hooft's UV-IR anomaly matching conditions; anomaly cancellation) - prof. Horatiu Nastase (May 30)
    • Lecture 25 (Chapter 58. The operator product expansion, renormalization of composite operators and anomalous dimension matrices) - prof. Horatiu Nastase (June 1)
    • Lecture 26 (Chapter 62. The Wilsonian effective action, effective field theory and applications) - prof. Horatiu Nastase (June 6)
    • Lecture 27 (Chapter 63. Kadanoff blocking and the renormalization group; connection with condensed matter) - prof. Horatiu Nastase (June 8)
    • Lecture 28 (Chapter 64. Lattice field theory) - prof. Horatiu Nastase (June 13)
    • Lecture 29 (Chapter 65. The Higgs mechanism) - prof. Ricardo Matheus (June 15)
    • Lecture 30 (Chapter 66. Renormalization of spontaneously broken gauge theories 1: the Goldstone theorem and Rξ gauges) - prof. Ricardo Matheus (June 20)
    • Lecture 31 (Chapter 67. Renormalization of spontaneously broken gauge theories II: The SU(2)-Higgs model) - prof. Ricardo Matheus (June 22)
    • Lecture 32 (Chapter 68. Pseudo-Goldstone bosons, nonlinear sigma model and chiral perturbation theory) - prof. Ricardo Matheus (June 27)
    * The video for lecture 6 is missing, so in this case there will be an actual lecture instead of a meeting, which will be recorded and added to the list.
  • Bibliography:
    [1] H. Nastase, "Introduction to quantum field theory", or the lecture notes for the second part (avaliable here).
    [2] M.E. Peskin and D.V. Schroeder, "An introduction to Quantum Field Theory"
    [3] L.H. Ryder, "Quantum Field Theory"
    [4] George Sterman, "An introduction to Quantum Field Theory"
    [5] Pierre Ramond, "Field theory: A modern primer"
    [6] Steven Weinberg, "The Quantum Theory of Fields"
    [7] Matthew D. Schwartz, "Quantum Field Theory and the Standard Model"
    [8] D. Bardin and G. Passarino, "The Standard Model in the Making"
  • Additional material:
     [a] R. Matheus notes on QFT II from previous iterations of the course (ugly, disorganized and covering less subjects, but with many explict calculations):
    • 2018 (more thoroughly fixed, but covers only half course, mainly path integrals and renormalization of abelian theories)
    • 2016 (more complete than 2018, but prefer the above if the subject is in both)
    • 2013 (no path integrals, but more extensive discussion of Non-Abelian theories - including one loop calculations. Prefer the above if the subject is in both.)
    [b] Loop corrections in the Standard Model: [c] Example Mathematica notebook: