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 most of Part I of the textbook as well as those sections of Part II and III that will allow us to introduce and discuss the most important aspects of abelian gauge theories. This will allow us to study all the main properties of a quantum theory of fields (QFT), elucidating the role it plays in providing a relativistic quantum theory of nature. We will study both path integral and canonical quantization, and introduce all the most important properties of a QFT up to its renormalizability and scaling behavior using the simple example of a scalar field theory. We will then extend the most important results to the case of spin-one-half and spin-one fields, and subsequently introduce the case of abelian gauge theories which will lead us naturally to the discussion of Quantum Electrodynamics. This will set the bases for further developments, mainly centered around non-abelian gauge theories and gauge symmetry breaking, to vbe 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
08/25 Syllabus. Introduction to QFT. [Text] (Sec.1), [SW](Ch.1)
08/27 Classical systems of fields: Lagrangian and Hamiltonian formalism. Noether's theorem. [Gol](Ch. 11), [PS](Sec. 2.2), [Text](Sec. 22), [BS], Notes
09/01 Lorentz group and Lorentz invariance. [Text](Sec. 2), [SW](Secs. 2.3-2.4, 5.6)
09/03 No class. Make-up class on Friday, 9/25.
09/08 Nother's currents and charges. Energy-momentum tensor. Angular momentum tensor. [Text](Sec. 22), [SW](Secs. 7.3-7.4), Notes
09/10 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. 3), [PS] (Sec. 2.3)
09/15 Klein-Gordon quantum field: energy and momentum, construction of physical states, generalization to the case of a complex scalar field. Spin-statistics theorem. [Text](Sec. 3 and 4), [PS] (Sec. 2.3)
09/17 No class. Make-up class on Friday 10/2.
09/22 The LSZ rduction formula. [Text](Sec. 5)
09/25 Conditions from the LSZ rduction formula: need for counterterms in the Lagrangian. [Text](Sec. 5)
09/29 Path integral in quantum mechanics. [Text](Sec. 6)
10/01 Path integral for the harmonic oscillator [Text](Sec. 7)
10/02 Path integral for a free theory. [Text](Sec. 8)
10/06 Path integral for an interacting field theory [Text](Sec. 9)
10/08 Path integral for an interacting field theory [Text](Sec. 9)
10/13 Scattering amplitudes and feynman rules [Text](Sec. 10)
10/15 Cross sections and decay rates. Kinematics in various reference frames, phase space integration. [Text](Sec. 11)
10/20 Cross sections and decay rates at tree level. [Text](Sec. 11)
10/22 Cross sections and decay rates including higher order corrections. Introduction to higher-order corrections and renormalizability. [Text](Sec. 12), your notes
10/27 g phi^3 theory (d=6): corrections to the propagator. [Text](Sec. 13-14. Read Sec. 15)
10/29 g phi^3 theory (d=6): corrections to the 3-point vertex, and to others 1PI vertices. Recap on higher-order corrections and renormalizability. [Text](Sec. 16-18)
11/03 g phi^3 theory (d=6): 2-particle scattering at 1-loop. Perturbation theory to all orders: skeleton expansion, introduction to the quantum action. [Text](Sec. 19-21)
11/05 Infrared divergences: general discussion of soft and collinear singularities. Role of real corrections in calculation of cross sections beyond tree level. [Text](Sec. 26, your notes)
11/10 Infrared divergences: application to the case of 2-particle elastic scattering in g phi^3 (d=6). [Text](Sec. 26)
11/12 Choosing a mass-independent renormalization scheme: minimal subtraction. Physical mass and coupling. Cancellation of IR divergences. [Text](Sec. 27)
11/17 Choosing a mass-independent renormalization scheme: minimal subtraction. Parameters in the Lagrangian (m,g) run with mass scale. [Text](Sec. 27)
11/19 No class. Make-up class on Friday 12/04.
11/24 Renormalization group. [Text](Sec. 28)
12/01 Spin 1 fields: review of Maxwell's equations. Quantization in Coulomb gauge. [Text](Secs. 54-55)
12/03 Spin 1 fields: LSZ reduction formula and path integral. [Text](Secs. 56-57)
12/04 Scalar electrodynamics: tree level and one-loop. [Text](Secs. 61,65-66)

[Text],[PS],[SW],[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 3:00 p.m. to 5:00 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 and will be distributed in class 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: Tue Dec 4 13:54:45 EST 2007