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.
Topics: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:
|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)|
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 available 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.