PHY 5669 : Quantum Field Theory B

Lectures: 12:30-1:45 pm, Tuesday and Thursday, in UPL 110.

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, and broad introduction to quantum field theory: For a very interesting historical introduction: And finally, an excellent reference for Group Theory:

Topics:

We will cover topics in Part II and III of the textbook, broadly indicated as Renormalization and Non Abelian Gauge Theories, with emphasis on those aspects that are of more interest to High Energy physicists. Concepts and results from Part I of the textbook (developed in QFT A) will be instrumental. The topics covered in this course are more naturally developed using the path integral quantization method, which we will introduce in the first lectures. We will move on to a systematic discussion of the renormalization of a generic field theory and study the renormalization group associated to it. This will allow us to efficiently develop the quantization of non-abelian gauge theories. After a general introduction to the problem, we will focus on the structure of Quantum Chromodynamics and of the Electroweak Theory.
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
01/09 Path Integral Methods in non-relativistic quantum mechanics [Text](Sec. 9.1), [SP](Sec. 2.1), [FS](Sec. 2.1)
01/08 Path Integral Methods in quantum field theory: correlation functions and generating functional. [Text](Sec. 9.2), [SP](Sec. 2.3), [FS](Sec.2.3)
01/20 Path Integral Methods in quantum field theory: perturbation theory and the generating functional. Your notes, [SP](Sec. 2.4), [FS](Sec.2.3)
01/22 Path Integral Methods in quantum field theory: quantization of the electromagnetic field, Faddeev-Popov method. [Text](Sec. 9.4), [SP](Sec. 3.1), [FS](Sec.3.1,3.3)
01/27 Path Integral Methods in quantum field theory: quantization of spinor fields; QED. [Text](Sec. 9.5), [SP](Sec. 2.5), [FS](Sec.2.4)
01/29 Systematics of Renormalization: structure of UV divergences by momentum power counting. Example: QED in d=4. [Text](Sec. 10.1), [SP](Sec. 4.2)
01/30 Systematics of Renormalization: definition and construction of a renormalized perturbation theory, counterterms and renormalized Lagrangian. [Text](Sec. 10.2), [SP](Sec. 4.1,4.2)
02/03 Systematics of Renormalization: renormalization of a scalar phi^4 type theory, explicit 1-loop calculation. [Text](Sec. 10.2), [SP](Sec. 4.3)
02/05 Systematics of Renormalization: renormalization of QED, explcit 1-loop calculation. [Text](Sec. 10.3), [SP](Sec. 5.2)
02/10 Renormalization and symmetry: Ward-Takahashi identities in QED. [Text](Sec. 9.6), [SP](Sec. 5.1)
02/17 Renormalization and symmetry: the Effective Action and its interpretation as the generating functional of the 1PI Green's functions. [Text](Sec. 11.3,11.5), [SW](Sec. 16.1)
02/19 Renormalization and symmetry: QED Ward-Takahashi identies in terms of the QED Effective Action and their implications. [SP](Sec. 5.1)
02/20 Renormalization Group: Wilson Approach to Renormalization Theory, I. [Text](Sec. 12.1)
02/24 Renormalization Group: Wilson Approach to Renormalization Theory, II. [Text](Sec. 12.1)
02/26 Renormalization Group Equation: solution, discussion of the calculation of beta and gamma's functions in the minimal subtraction scheme. [Text](Sec. 12.2, first part), [SP](Sec. 6.1),
[SW](Ch. 18)
03/02 Renormalization Group Equation: calculation of beta and gamma's functions for a real scalar phi^4 theory. [SP](Sec. 6.2)
03/04 Renormalization Group Equation: calculation of the beta of QED, effective coupling constant, expansion in leading logarithms. [SP](Sec. 6.3)
03/16 Non-Abelian Gauge Theories: the geometry of gauge invariance. [Text](Sec. 15.1)
03/18 Non-Abelian Gauge Theories: the Yang-Mills Lagrangian. [Text](Sec. 15.2)
03/23 Quantum Non-Abelian Gauge Theories: Feynman rules for fermions and gauge bosons, Faddeev-Popov method. [Text](Sec. 16.1-16.2)
03/25 Quantum Non-Abelian Gauge Theories: ghost fields and unitarity. [Text](Sec. 16.2-16.3)
03/30 Quantum Non-Abelian Gauge Theories: renormalization and beta-function. [Text](Sec. 16.5)
04/01 Quantum Chromodynamics: some puzzling experimental facts. [Text](Ch. 14, Sec. 17.2)
04/06 Quantum Chromodynamics: theoretical structure and its implications. [Text](Sec. 17.1-17.2)
04/08 Quantum Chromodynamics: Deep Inelastic Scattering, Parton Distribution Functions. [Text](Sec. 17.3)
04/13 Quantum Chromodynamics: Hard scattering processes in hadron collisions [Text](Sec. 17.4)
04/15 Quantum Chromodynamics: Parton Evolution: Altarelli-Parisi equations. [Text](Sec. 17.5)
04/20 The Electroweak Theory: gauge theories with spontaneous symmetry breaking. [Text](Sec. 20.1)
04/22 The Electroweak Theory: the lagrangian of the Glashow-Weinberg-Salam theory. [Text](Sec. 20.2), [SW] (Ch. 21)

[Text],[IZ],[SW],[SP],[FS],[PR],[Ry] : see above

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 will be a take home exam. The exam is now available and the solution will have to be returned to me during the final exam week no later than Friday April 30th, 2004.

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