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 less technical but very up-to-date and intriguing introduction to quantum field 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 be seen in the second part of the course, Quantum Field Theory B. An updated summary of the topics covered in class will be given on this web page.

Date Topics covered Reference
08/26 Syllabus. Introduction to QFT. Classical systems of fields: Lagrangian and Hamiltonian formalism. [Text] (Ch. 1), [SW](Ch.1), [Gol](Ch. 11), [PS](Sec. 2.2)
08/28 Noether's theorem in classical field theory. [PS](Sec. 2.2), [Text](Ch. 22), [BS], Notes
09/02 Lorentz group and Lorentz invariance. Nother's currents and charges. Energy-momentum tensor. Angular momentum tensor. [Text](Ch. 2, 22), [SW](Secs. 2.3-2.4, 2.5, 7.3-7.4), Notes
09/04 Lagrangian for a classical real scalar field, Klein-Gordon equation, energy and momentum of a system of classical real scalar fields. [Text](Ch. 3), [PS] (Sec. 2.3)
09/09 Klein-Gordon quantum field: quantization, construction of physical states. Spin-statistics theorem. [Text](Ch. 3 and 4), [PS] (Sec. 2.3)
09/11 Klein-Gordon quantum field: generalization to the case of a complex scalar field. Your notes.
09/16 Computing scattering amplitudes of the interacting theory: the LSZ reduction formula. Correlation functions of the interacting theory as fundamental building blocks of scattering amplitudes. [Text](Sec. 5)
09/18 Conditions from the LSZ reduction formula: need for a reparametrization of the Lagrangian, fisrt hint at renormalization of fields and couplings. [Text](Sec. 5)
09/23 Calculating correlation functions of the interacting theory: brief review of canonical approach (it would be useful for you to try Problem 9.5 of Homework 3 before this lesson), introduction to path-integral quantization. [Text](Problem 9.5, Secs. 6 and 7.)
09/30 Path integral for a free theory. [Text](Sec. 8)
10/02 Path integral for an interacting field theory: calculating the functional integral. [Text](Sec. 9)
10/07 Path integral for an interacting field theory: Feynman diagrams and Feynman rules. [Text](Sec. 9)
10/09 Path integral for an interacting field theory: counterterm Lagrangian. [Text](Sec. 9)
10/14 Scattering amplitudes and feynman rules [Text](Sec. 10)
10/16 Cross sections and decay rates. Kinematics in various reference frames, phase space integration. [Text](Sec. 11)
10/21 Cross sections and decay rates at tree level. [Text](Sec. 11)
10/23 Cross sections and decay rates including higher order corrections. Introduction to higher-order corrections and renormalizability. [Text](Sec. 12), your notes
10/28 g phi^3 theory (d=6): corrections to the propagator. Dimensional regularization. [Text](Sec. 13-14. Read Sec. 12, 15). [PS] (parts of Secs. 6.3, 7.5, and App. A.4)
10/30 g phi^3 theory (d=6): corrections to the 3-point vertex, and to others 1PI vertices. [Text](Sec. 16)
11/04 No class
11/06 No class
11/07 Make-up class: 10:15-11:30 am in Keen 707. Recap on higher-order corrections and renormalizability. g phi^3 theory (d=6): 2-particle scattering at 1-loop. [Text](Secs. 17-20)
11/13 Perturbation theory to all orders: skeleton expansion.
Infrared divergences: general discussion of soft and collinear singularities. Role of real corrections in calculation of cross sections beyond tree level.		 [Text](Sec. 19-21),
[Text](Sec. 26, your notes)
11/18 No class
11/20 Classes have been cancelled campus wide
11/21 Make-up class: 12:00-1:15 pm in Keen 707. Infrared divergences: application to the case of 2-particle elastic scattering in g phi^3 (d=6). [Text](Sec. 26)
11/24 Make-up class: 12:00-1:15 pm in Keen 707. Choosing a mass-independent renormalization scheme: minimal subtraction. Physical mass and coupling. Cancellation of IR divergences. [Text](Sec. 27)
11/25 Choosing a mass-independent renormalization scheme: minimal subtraction. Parameters in the Lagrangian (m,g) run with mass scale. [Text](Sec. 27)
12/02 Renormalization group. [Text](Sec. 28) WK-paper
12/04 Spin 1 fields: review of Maxwell's equations. Spin 1 fields: LSZ reduction formula and path integral. [Text](Secs. 54-57)
12/05 Make-up class: 12:00-1:15 pm in Keen 707 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 2:30 p.m. to 4:30 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., traveling due to research work, conferences, religious holiday, etc.) 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.