Regular Courses
at IFT (mostly portuguese)
Quantum Field Theory I  2º Semester, 2020
 Credits: 12 (in "hours per week")
Prerequisites: Classical Field Theory
Meetings: Tuesdays and Thursdays, 14:00 to 16:00

Overview:
We will go through the syllabus below following (with small deviations) the order of ref [1] (below) but keeping a notation and conventions much closer to ref [2] (which is also used by many other QFT books). It is assumed that students have already studied (relativistic) Classical Field Theories, and only a very limited review of them will be offered.
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:
Due to the COVID19 crisis, I'm testing a new way of offering the course (which might be maintained afterwards, depending on the degree of success  or failure). 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 present the exercises.
Below are the links to the videolectures 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 timestamp 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.

Execises:
For the lectures the exercises are not listed here, they are included in the lectures themselves (in the last few minutes of the video).

Syllabus:
(I) Functional Methods
Path Integrals in Quantum Mechanics, the Harmonic Oscillator
(II) Canonical Quantization
Canonical Quantization of Scalar Fields
Propagators
Interaction Picture and Wick's Theorem
Feynman Rules
(III) Path Integral Quantization in Field Theory
Wick's Theorem (Scalar field, with Path Integrals)
Feynman Rules (Scalar field, with Path Integrals)
Quantization of the Dirac Field and Feynman rules for fermions
Spin Sums
Quantization of Gauge Fields (mostly Abelian)
(IV) Processes and Observables in QFT
Scattering cross sections and the S matrix
Feynman diagrams for the S matrix
Optical theorem
Simple processes in QED
(Coulomb potential, Rutherford scattering, electronpsitron annihilation)

Student Seminars:
Students are supposed to prepare a 40 minute seminar by the end of the course. The subject should be something beyond what has been discussed in the course, but which is a smooth extention of it.
Dates and subjects are listed below:
Monday, 14th of December, 2020:
 13:00  Compton Scattering (file)  Matheus Da Luz Cravo
 14:00  QFT at finite temperature (file)  Benjamin Garcia De Figueiredo
 15:00  Graphene and Dirac Fermions in 2+1 dimensions (file)  Lars Wolfram Dehlwes
 16:00  Representations of the Lorentz Group in Quantum Mechanics (file)  Felipe Augusto da Silva Barbosa
 17:00  Majorana Fermions (file)  Wescley De Carvalho Dimas
Tuesday, 15th of December, 2020:
 13:00  The Casimir Effect (file)  João Caetano Oliveira Carvalho
 14:00  Renormalization in the Ising Model (file)  Pedro Fittipaldi De Castro
 15:00  Expontaneous Symmetry Breaking and the Goldstone Theorem (file)  Marcello Vinícius Hallas Cemin
 16:00  Higgs Mechanism (file notes)  Rodrigo Teixeira Aguiar
 17:00  The Unruh Effect (file)  Alan Müller
 Bibliography:
[1] H. Nastase, "Introduction to Quantum Field Theory", and lecture notes (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"
 Additional material:
[a] V. Kaplunovsky, Dirac Matrices and Lorentz Spinors (avaliable here).
[b] Some references to stationary phase methods (in growing level of mathematical rigor): Cohn; Zelditch; Petersen.
The canonical reference is: L. Hörmander, "The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis", sect 7.7.
[c] Jaffe's piece on Natural Units
[d] Some old notes of mine on Functional Derivatives.
[e] Some short and yet (more) formal treatment of Grassmann numbers (in growing level of mathematical rigor): PlanetMath entry for supernumbers; Wikipedia entry is not bad; first few sections of this Philbin paper.
The canonical reference is: B. DeWitt, "Supermanifolds".
[g] About Fierz identities: T. Brauner, "Fierz transformations" (avaliable here).
[h] A step up in rigor from Peskin's treatment of CTP symmetries and spinors by Kevin Cahill (even more detail here). The most rigorous treatment can be found in ref [6], chapter 5.
[i] Interesting discutions about the foundations and validity of Quantum Field Theories: focusing on Haag's Theorem and Perturbative Series & Renormalization.