Regular Courses at IFT (Portuguese and English)

Quantum Field Theory II - 1st Semester, 2024

  • Credits: 12 (in "hours per week")
    Prerequisites: Quantum Field Theory I (specifically the subjects covered here)
    Meetings: twice a week (according to this schedule)
  • Overview:
    We will go through the syllabus below keeping a notation and conventions closer to ref [2] (which is also used by many other QFT books). It is assumed that students have already studied Quantum Field Theory, understand the quantization of field theories both in the canonical and path integral approaches and are capable of calculating tree level processes. This course is (finally) a natural continuation of the QFT I course I offered in the last three years, therefore details on the subjects already covered can be found here.

    Grades will be based on exercises, active participation in the meetings and a seminar (to be given by each student at the course's end).
  • Video lectures:
    We will not have in-class lectures per se. There will be videos (one or two videos per lecture) on YouTube, and the students are expected to watch them and work through the exercises. This can be very profitable for students as long as an active stance is taken (and it will be total crap for passive students, beware). Take full advantage of watching the lecture in video format: stop, rewind, skip, check notes and references as needed, speed up the video when I'm going too slow (as is often the case).

    You can use the Visual Subject Guide to quickly navigate through the videos (clicking on the PDF will take you to the corresponding video). 

    Twice a week there will be a meeting/lecture in which the students are expected to discuss the subjects in the videos and present the exercises. The discussion will be only profitable to those that did prepare properly.

    Below are the links to the videos needed for each lecture and the corresponding pages in my lecture notes.

    Attention: the lecture notes are in Portuguese (and will probably never get translated - there is already plenty of good material in English) and are intended more as an organizational tool for myself, and sometimes are used to make reference to equations in the exercises (it is easier than giving a time-stamp on a video). There are certainly many mistakes in these notes and they are badly organized. Use them only as a map to see what we are discussing, go to the bibliography for the real thing.
  • Exercises:
  • Syllabus:
    (I) Radiative Corrections
            Källén-Lehmann Spectral Representation
            LSZ Reduction Formula
            The relation between observable quantities and Lagrangian parameters
           
    (II) Renormalization
            Counting Ultraviolet Divergences
            Perturbative Renormalization

    (III) Renormalization Group Equations
            Callan-Symanzik equation
            Running of coupling constants and mass renormalization

    (IV) Quantization of non-Abelian Gauge Theories
            Faddeev-Popov method
            Faddeev-Popov ghosts and unitarity;
            Quantum Chromodynamics (QCD) and renormalization; asymptotic freedom

  • Bibliography:
     [1] H. Nastase, "Introduction to Quantum Field Theory"
    [2] M.E. Peskin and D.V. Schroeder, "An introduction to Quantum Field Theory"
    [3] L.H. Ryder, "Quantum Field Theory"
    [4] G. Sterman, "An introduction to Quantum Field Theory"
    [5] P. Ramond, "Field theory: A modern primer"
    [6] S. Weinberg, "The Quantum Theory of Fields"
    [7] M. D. Schwartz, "Quantum Field Theory and the Standard Model"
    [8] T.-P. Cheng and L.-F. Li, "Gauge theory of elementary particle physics"
    [9] A. Zee, "Quantum Field Theory in a Nutshell"
  • Additional material:
     [a] V. Kaplunovsky, Dirac Matrices and Lorentz Spinors (available here).
    [b] Jaffe's piece on Natural Units
    [c] Interesting discussions about the foundations and validity of Quantum Field Theories: focusing on Haag's Theorem and Perturbative Series & Renormalization.
    [d] Marco Serone, Spectral representation for fermions: Notes on Quantum Field Theory, sec. 2.1.3.