PHY 5667 : Quantum Field Theory A

Lectures: 11:00-12:15, Tuesday and Thursday, Keen 701.

Professor : Laura Reina, 510 Keen Building, 644-9282, e-mail: click here

Texts :

Other suggested reference books: For a non technical and very up to date intriguing introduction to quantum field theory: For a very interesting historical introduction: And finally, an excellent reference for Group Theory:


We will cover the first seven chapters of the textbook. This will allow us to introduce the classical and quantum theory of fields, the role of global and local (or gauge) symmetries, and to discuss in detail the case of Quantum Electrodynamics (QED), one of the most successful theories of modern and contemporary Physics. We will explicitly show the renormalizability of the theory, and calculate several physical observables thoroughly. This will set the basis for further developments to be seen in the second part of the course, Quantum Field Theory B. Here is a summary of the topics that have been covered in class so far or that will be covered in the next coming lectures:

Date Topics covered Reference
08/29 Syllabus. Introduction to QFT. Natural Units. [PS] (Ch.1), [SW](Ch.1), your notes.
08/31 Classical systems of fields: Lagrangian and Hamiltonian formalism. Euler-Lagrange equations. [PS](Sec. 2.2), [MM] (Sec. 3.1), [Gol](Ch. 11).
09/05 NO CLASS
09/07 Lagrangian for a classical real scalar field, Klein-Gordon equation. Noether's theorem in classical field theory. [PS] (Sec. 2.2), [MM](Sec. 2.7), [BS], Notes. [MM] Chapter 2.
09/12 CLASS CANCELED due to weather conditions
09/14 CLASS CANCELED due to weather conditions
09/19 Noether's theorem in classical field theory, continued. Energy-momentum tensor for a system of fields. [PS] (Sec. 2.2), [MM](Sec. 2.7), [BS], Notes. [MM] Chapter 2.
09/21 To make up for all lessons canceled last week, from today we will meet from 10:45 a.m. till 12:30 p.m. (i.e. 30 extra minutes).
09/21 Lorentz invariance. Angular momentum tensor and associated charges. [PS] (Sec. 2.2), [MM](Sec. 2.7), [BS], Notes. [MM] Chapter 2.
09/26 Klein-Gordon quantum field: quantization, Hamiltonian and momentum operators, number density operator. [PS] (Sec. 2.3), [MM](Sec. 4.1)
09/28 Klein-Gordon quantum field: construction of physical states and their interpreation. Generalization to the case of a complex scalar field, conserved charge, physical states. [PS](Problem 2.2 and Secs. 2.3-2.4), [MM] (Secs. 3.3.2, 4.1.2)
10/03 Klein-Gordon quantum field: Feynman propagator. [PS](Secs. 2.4), [MM] (Sec. 5.4)
10/05 Introduction to theories of interacting fields. Towards a perturbative expansion of correlation functions. [PS] (Secs. 4.1 and 4.2), [MM] (Secs. 5.3)
10/10 Interacting fields: Perturbative expansion of correlation functions. [PS](Secs. 4.2), [MM] (Secs. 5.3)
10/12 Wick's theorem, introduction to Feynman diagrams. [PS] (Secs. 4.3-4.4), [MM] (Sec. 5.5)
10/17 Correlation functions as sum of connected Feynman diagrams. [PS](Sec. 4.4)
10/19 The S matrix. S-matrix elements and the LSZ reduction formula. [PS] (Secs. 4.5), [MM] (Sec. 5.1-5.2)
10/24 Computing S-matrix elements from Feynman diagrams. [PS] (Secs. 4.6), [MM] (Sec. 5.5.1)
10/26 Cross section for a 2->n scattering process (scalar fields). [PS] (Sec. 4.5 and 7.2), [MM] (Sec. 6.2-6.4)
10/31 Lorentz Group and its representations. Classification of fields: scalar, spinor, and vector fields as different representations of the Lorentz Algebra. [Text](Secs. 3.1), [MM](Sec. 2.4-2.6), [SW](Sec.2.3,2.4,5.6)
11/02 Homework discussion: linear sigma model. Introduction to spinor fields: Weyl spinors/equation. [PS] (Sec. 3.2), [MM] (Secs. 3.4.1-3.4.4).
11/07 Starting today we will resume our regular class time: 11:00 a.m. to 12:15 p.m.
11/07 Introduction to spinor fields: Dirac spinors, Dirac Lagrangian, Dirac equation. [PS] (Sec. 3.2), [MM] (Secs. 3.4.1-3.4.4).
11/09 NOTICE: today we meet in Keen 503.
11/09 Introduction to spinor fields: symmetries of the Dirac Lagrangian; Majorana spinors. [PS] (Sec. 3.2), [MM] (Secs. 3.4.1-3.4.4).
11/14 Classical solutions of the Dirac equation, detailed calculation and discussion of the results. [PS] (Sec. 3.3), [MM] (Secs. 3.4.2).
11/16 Quantization of Dirac fields, construction of physical states. Spin-statistics relation. [PS] (Sec. 3.5), [MM] (Sec. 4.2)
11/21 Dirac field propagator. Feynman rules for fermions. Interacting theory of fermions and scalars. [PS](Secs. 3.5 and 4.7)
10/28 Quantization of the electromagnetic field: covariant quantization. [PS](Sec. 4.8), [MM] (Sec. 4.3)
11/28 MAKE-UP CLASS: KEEN 701, 12:15-1:30 p.m.
QED Lagrangian from gauge symmetry principle. QED Feynman rules. Calculation of tree level cross sections in QED. Examples: e+ e- -> mu+ mu-.
[PS] (Sec. 4.1, 4.8, 5.1, 5.3), [MM] (Sec. 7.1, 7.3)
11/30 NO CLASS
12/05 Introduction to radiative corrections in QED. Cross section for e+ e- -> mu+ mu- beyond the tree level: O(alpha) virtual and real corrections. UV and IR divergences, origin and general treatement. Your notes, [PS] (Introduction to Chapter 6)
12/06 MAKE-UP CLASS: KEEN 701, 4:30-6:00 p.m.
The electron self-energy, detailed calculation of the one-loop correction. Feynman parametrization of loop integrals. Pauli-Villars regularization. Dimensional regularization. Presence of IR divergences. Relation to field and mass renormalization. Brief discussion of photon self-energy and vertex corrections.
[PS] (Parts of Secs. 7.1, 7.2, 7.5, 6.2, and 6.3)
12/07 Summary of the results obtained and explicit discussion of QED renormalization (fields, mass, and charge renormalization), at one-loop (explicit) and in general (starting from the QED Lagrangian). [PS] (Parts of Secs. 7.2, and 10.3)

[MM],[PS],[SW], [Sr], [IZ],[Scw],[Ry] : see above
[Gol] : H. Goldstein, C.P. Poole and J.L. Safko,Classical Mechanics, Addsion-Wesley Publishing Co.
[BS] : N.N. Bogoliubov and D.V. Shirkov, Introduction to the Theory of Quantized Fields, John Wiley and Sons Ed.

Office Hours: Tuesday, from 1:30 p.m. to 3:30 p.m.

You are also welcome to contact me whenever you have questions, either by e-mail or in person.


A few homeworks will be assigned during the semester, tentatively every other week. The assignments and their solutions will be posted on this homepage.

Exams and Grades.

The grade will be based 70% on the homework and 30% on the Final Exam, and will be roughly determined according to the following criterium:

100-85% : A or A-
84-70% : B- to B+
below 70% : C

Attendance, participation, and personal interest will also be important factors in determining your final grade, and will be used to the discretion of the instructor.

The Final exam is a take-home exam and will be available two weeks before Final Exam week, to be returned on a date that will be specified at that time.

Attendance. Regular, responsive and active attendance is highly recommended. A student absent from class bears the full responsibility for all subject matter and information discussed in class.

Absence. Please inform me in advance of any excused absence (e.g., religious holiday) on the day an assignment is due. In case of unexpected absences, due to illness or other serious problems, we will discuss the modality with which you will turn in any missed assignment on a case by case basis.

Assistance. Students with disabilities needing academic accommodations should: 1) register with and provide documentation to the Student Disability Resource Center (SDRC); 2) bring a letter to me from SDRC indicating you need academic accommodations and what they are. This should be done within the first week of class. This and other class materials are available in alternative format upon request.

Honor Code. Students are expected to uphold the Academic Honor Code published in the Florida State University Bulletin and the Student Handbook. The first paragraph reads: The Academic Honor System of Florida State University is based on the premise that each student has the responsibility (1) to uphold the highest standards of academic integrity in the student's own work, (2) to refuse to tolerate violations of academic integrity in the University community, and (3) to foster a high sense of integrity and social responsibility on the part of the University community.

Laura Reina
Last modified: Mon Aug 29 17:35:45 EST 2016