PHY 5669 : Quantum Field Theory B

Lectures: 11:00-12:15, Tuesday and Thursday, UPL 109.

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

Office Hours: Tuesday, from 1:00 p.m. to 3:00 p.m.

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

Text :

Other suggested reference books: For a non technical and very up to date intriguing introduction to quantum field theory: And finally, an excellent reference for Group Theory:


We will cover topics in Part II and III of Pskin ansd Schroeder's book, 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 QFT A (developed using both Peskin and Schroeder's and Maggiore's books) 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 lectures:

Make-up class: 2:00-3:30 PM, 503 Keen.
Date Topics covered Reference
01/10 Systematics of Renormalization: structure of UV divergences by momentum power counting. Example: QED in d=4. [PS](Secs. 10.1, 10.3)
01/12 Systematics of Renormalization in generic d dimensions. Example: QED and phi^4 theory. Definition and construction of a renormalized perturbation theory: cancellation of UV-regulator order by order when using physical parameters, sistematically obtained by using counterterms and renormalized Lagrangian. [PS](Secs. 10.2, 10.3)
01/17 Renormalization and symmetry: Ward-Takahashi identities in QED. [PS](Secs. 7.4, 10.3)
01/19 Introduction to path-integral quantization. [PS] Section 9.1. [Sr] Chapter 6-7.
01/24 Path-integral methods in quantum field theory: correlation functions in terms of functional integrals. [PS] Section 9.2, [Sr] Chapter 8.
01/26 Path-integral methods in quantum field theory: generating functional and correlation functions. [PS] Section 9.2, [Sr] Chapter 8.
01/31 Path-integral methods in quantum field theory: perturbation theory and the generating functional. Your notes, [Sr] Chapter 9.
02/01 Path Integral Methods in quantum field theory: quantization of the electromagnetic field, Faddeev-Popov method. [Text] Sec. 9.4, [Sr] Chapter 57.
02/06 Path Integral Methods in quantum field theory: quantization of spinor fields; QED. [Text] Sec. 9.5, [Sr] Chapter 43.
02/08 Path Integral Methods in quantum field theory: symmetries and Ward-Takahashi identities. [Text] Sec. 9.6.
02/14 Renormalization Group: Wilson Approach to Renormalization Theory, I. [PS] Section 12.1, WK-paper
02/16 Renormalization Group: Wilson Approach to Renormalization Theory, II. [PS] Section 12.1, WK-paper
02/20 Make-up class: 3:45-5:00 PM, 503 Keen. Renormalization Group: Callan-Symanzik equation, definition of beta-function, mass anomalous dimension, and field anomalous dimension. [PS] Section 12.2, [Sr] Chapter 27.
02/21 Renormalization Group: solution of RGE, discussion of the calculation of beta and gamma's functions in the minimal subtraction scheme. Example: phi^4 theory. [PS] Section 12.2, [Sr] Section 28, your notes.
02/23 Renormalization Group: calculation of the beta function of QED, effective coupling constant, expansion in leading logarithms. [PS] Section 12.3, your notes
02/28 Special time: 12:30-1:45 PM, 503 Keen. Non-abelian gauge theories: introduction. [PS] Sections 15.1-15.2 (Section 15.3: read as reference)
03/02 Non-abelian gauge theories: the Yang-Mills Lagrangian. [PS] Sections 15.2 and 16.1
03/07 Quantum Non-Abelian Gauge Theories: Faddeev-Popov method, ghost fields and unitarity.[PS] Sections 16.2-16.3
03/09 Quantum Non-Abelian Gauge Theories: renormalization and beta-function. [PS] Section 16.5
03/14 Spring Break
03/16 Spring Break
03/21 Introduction to QCD: theoretical structure and its implications. Puzzling experimental facts merge with new theoretical developments. [PS] Sections 14 and 17.1-17.2
03/23 Quantum Chromodynamics: Deep Inelastic Scattering, Parton Distribution Functions. [PS] Section 17.3
03/23 Quantum Chromodynamics: Hard scattering processes in hadron collisions, general structure. [PS] Sections 17.4
03/28 NO CLASS Work on Homework 5
03/30 NO CLASS Work on Homework 5
04/04 Gauge theories with spontaneous symmetry breaking, abelian case. [PS] Section 20.1. Look also at Section 11.1.
04/05 Make-up class: 9:30-11:00 PM, 503 Keen. Gauge theories with spontaneous symmetry breaking, understanding of the physical spectrum (gauge bosons and scalars). [PS] Section 20.1
04/06 NO CLASS Work on Homework 5!
04/11 Gauge theories with spontaneous symmetry breaking, non-abelian case. [PS] Section 20.1
04/12 Make-up class: 9:30-11:00 PM, 503 Keen. SSB and electroweak interactions: towards the Standard Model of particle physics. [PS] Section 20.2
04/13 NO CLASS Work on Homework 5!!!
04/18 NO CLASS
04/19 Make-up class: 9:30-11:00 PM, 503 Keen. The Glashow-Weinberg-Salam theory or Standard Model: gauge boson mass eigenstates, electroweak currents. [PS] Section 20.2
04/20 The Glashow-Weinberg-Salam theory or Standard Model: fermion masses, flavor mixing, and the origin of CP-violation. [PS] Sections 20.2 and 20.3
04/25 Quantization of SSB gauge theories: abelian case, definition of R-csi gauges. [PS] Section 21.1
04/27 Quantization of SSB theories: non-abelian case. Quantum structure of the GWS theory. Precision fits. [PS] Section 21.1. 21.3, SM-Lecture-1, SM-Lecture-2, SM-Lecture-3, SM-Lecture-4

[MM],[PS],[SW], [Sr], [IZ],[Scw],[Ry] : see above


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 available approximately two weeks before Final Exam week, to be returned on a date that will be specified at that time. The Final Exam is now available. It is a take-home exam, and will have to be turned in by Friday, May 5th, 2017 at the latest. In the following you will find links to references that can help you figuring out the SM Feynman rules and some of the calculations of your Final exam. The references contain much more than you actually need (they all discuss loop calculations in the Standard Model), but they have nice introductory sections on the Standard Model Lagrangian, they discuss the choice of gauge, and they give a complete set of Feynman rules for a given gauge choice. Use them as references! You do not have to follow them exactly, but they can help you understanding and answering many questions.

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