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

Textbook and suggested references:

Textbooks used in the past: 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: An excellent reference for Group Theory:

Topics:

Quantum field theory (QFT) is fundamental to understanding contemporary theoretical physics and its evolution over the last several decades. In this class we will introduce the classical and quantum theory of fields, the role of global and local (or gauge) symmetries, the application of QFT to the calculation of scattering amplitudes.
In this class we will cover most of Part I of the textbook [M. Sredniki, Quantum Field Theory] 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, 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 selected 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

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
08/27 Syllabus. [Sr] (Ch. 1), [MS] (Ch.1), [SW] (Ch.1)
08/29 NO CLASS.
Review Lorentz transformations and Lorentz invariance. 		[Sr] (Ch. 2), [MS] (Ch. 2), [MM] Chapter 2
09/03 Introduction to QFT. Natural Units. Classical systems of field, Euler-Lagrange equations. [Gol] (Ch. 11), [PS] (Sec. 2.2)
09/05 Lagrangian for a classical real scalar field, Klein-Gordon equation. [Sr] (Ch. 3), [PS] (Sec. 2.3)
09/06 MAKE-UP CLASS: 11:00 AM, Keen 701
Klein-Gordon quantum field: quantization, construction of physical states. 		[Sr] (Ch. 3 and 4), [PS] (Sec. 2.3)
09/10 Computing scattering amplitudes of the interacting theory: the LSZ reduction formula. Correlation functions of the interacting theory as fundamental building blocks of scattering amplitudes. [Sr] (Ch. 5)
09/12 Conditions from the LSZ reduction formula: need for a reparametrization of the Lagrangian, first hint at renormalization of fields and couplings. [Sr] (Ch. 5)
09/13 MAKE-UP CLASS: 11:00 AM, Keen 701
Discussion of Problem 3.5: complex scalar field, U(1) global invariance, conserved charge. Noether's theorem for the case of field transformations. 		[Sr] (Ch. 3, 22). Your Notes.
09/17 Introduction to path-integral quantization. [Sr] (Ch. 6)
09/19 Properties of the path-integral in quantum mechanics. [Sr] (Ch. 6)
09/24 NO CLASS.
09/26 NO CLASS.
10/01 Path integral for a free theory. [Sr] (Ch. 8)
10/03 Two-point correlation function: detailed calculation in both canonical and path-integral formalism. Feynman propagator. [Sr] (Ch. 8), [MS] (Sec. 6.2), your notes.
10/08 Path integral for an interacting field theory: calculating the generating functional. [Sr] (Ch. 9)
10/10 Path integral for an interacting field theory: Feynman diagrams and Feynman rules. [Sr] (Ch. 9)
10/11 MAKE-UP CLASS: 11:00 AM, Keen 701
Path integral for an interacting field theory: counterterm Lagrangian.		 [Sr](Ch. 9)
10/15 From correlation functions to scattering amplitudes and Feynman rules [Sr](Ch. 10)
10/17 Scattering amplitudes and Feynman rules [Sr](Ch. 10)
10/22 Cross sections and decay rates. Kinematics in various reference frames, phase space integration. [Sr](Ch. 11)
10/24 Cross sections and decay rates at tree level. [Sr](Ch. 11)
10/29 Cross sections and decay rates including higher order corrections. Introduction to higher-order corrections and renormalizability. [Sr](Sec. 12), your notes
10/31 Exact propagator: Lehman-Kaellen form. g phi^3 theory (d=6): corrections to the propagator. [Sr](Ch. 13-14). [PS] (parts of Secs. 6.3, 7.5, and App. A.4)
11/01 MAKE-UP CLASS: 2:30 PM, Keen 701
g phi^3: Self-energy calculation at one loop, dimensional regularization. 		[Sr] (Ch. 14). [PS] (parts of Secs. 6.3, 7.5, and App. A.4)
10/05 g phi^3 theory (d=6): corrections to the 3-point vertex, and to others 1PI vertices. [Sr] (Ch. 16)
11/07 Recap on higher-order corrections and renormalizability. g phi^3 theory (d=6): 2-particle scattering at 1-loop. [Sr] (Ch. 17-20)
11/12 Problems with massless theories: IR divergences and zero-mass limit of OS scattering amplitudes. A mass-independent renormalization scheme: minimal subtraction. Relation between OS and MS schemes. [Sr] (Chs. 26-27)
11/14 MS scheme: parameters in the Lagrangian (m,g) run with mass scale. UV and IR asymptotic regimes of a given QFT, probing the validity of a perturbative solution. [Sr] (Ch. 27)
11/19 Renormalization group. [Sr] (Ch. 28) WK-paper
11/21 Infrared divergences and their cancellation at the level of inclusive cross sections: general discussion. [Sr] (Ch. 26)
11/26 Infrared divergences and their cancellation at the level of inclusive cross sections: the case of 2-particle elastic scattering in g phi^3 (d=6). [Sr] (Ch. 26)
12/03 Scalar electrodynamics from a U(1) gauge invariance principle. [Sr] (Ch. 61)
12/05 Spin 1 fields in a nutshell. Scalar electrodynamics: Feynman rules. Brief discussion of Final Exam. [Sr] (Ch. 54-57, 65-66)
12/10 Extra discussion and Q/A session: 11:00 AM, Keen 701
 [Sr] (Ch. 65-66)

[MS], [PS], [MM], [SW], [Sr], [Scw], [IZ], [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.

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 now available! It is a take-home exam and will have to be returned no later than Friday Dec. 13 at 5:00 PM.

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: Wed Aug 22 7:51:54 EST 2018