PHY 5667 : Quantum Field Theory A

Lectures: 11:00-12:15, Tuesday and Thursday, in UPL 107.

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

Text :

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:

Topics:

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 lecture:

Date Topics covered Reference
08/24 Syllabus. Introduction to QFT and QED. [SW](Ch.1), [Scw]
08/26 Classical systems of fields: Lagrangian and Hamiltonian formalism. Examples: real and comples scalar field (Klein-Gordon field). [Gol] (Ch. 11), [Text](Sec. 2.2), [Ry](Sec. 3.1)
08/31 Classical systems of fields: Noether's theorem. Energy-momentum tensor, angular momentum tensor. [Text](Sec. 2.2), [Ry](Sec. 3.2), [BS]
09/02 Klein-Gordon quantum field: quantization of a system of real scalar fields, annihilation and creation operators. Comments on generalization to the case of a complex scalar field. [Text](Sec. 2.3)
09/07 FSU CLOSED: CLASS CANCELED
09/9 Klein-Gordon quantum field: Hamiltonian and momentum operators, number density operator, physical spectrum. Time evolution of field operators: Heisemberg representation. [Text](Secs. 2.3-2.4)
09/14 Klein-Gordon quantum field: Feynman propagator, detailed discussion. [Text](Sec. 2.4)
09/16 FSU CLOSED: CLASS CANCELED.
09/21 Lorentz Group and its representations. [Text](Sec. 3.1), [SW](Secs.2.3,2.4,5.6)
09/23 Study of the spinor representation of the Lorentz Group. Dirac equation. [Text](Sec. 3.2)
09/28 Dirac Lagrangian. Vector and axial curents. Properties of gamma matrices. [Text](Secs. 3.2,3.4)
09/30 Study of the solutions of the Dirac equation. Quantization of the Dirac field: what doesn't work if using commutation relations. [Text](Secs. 3.3, 3.5)
10/05 Quantization of the Dirac field: spin operators, spin quantum number of physical states. Dirac field propagator. [Text](Sec. 3.5)
10/07 Introduction to theories of interacting fields. [Text](Sec. 4.1)
10/12 Interacting fields: perturbative expansion of correlation functions. [Text](Secs. 4.2)
10/14 Interacting fields: Wick theorem, introduction to Feynman diagrams. [Text](Secs. 4.3-4.4)
10/19 Interacting fields: correlation functions as sum of connected Feynman diagrams. [Text](Sec. 4.4)

[Text],[IZ],[SW],[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: Wednesday, from 2:00 p.m. to 4:00 p.m.

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

Homework:

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. The solutions of the exam have to be placed in my mail box by Thursday December, 9 2004, at 12:00 p.m. I will be available for question as well as extra discussion meetings during exam week.

Here is a detailed summary of your grades.

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: Thu Dec 16 08:16:08 EST 2004