PHY 5667 : Quantum Field Theory A

Lectures: 11:00-12:15, Tuesday and Thursday, MCH 220.

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

Texts :

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: And finally, an excellent reference for Group Theory:

Topics:

This is an introductory class in Quantum Field Theory (QFT), and for many students the only class on this subject during their graduate studies. For this reason this year we will try a new approach, which introduces two main textbooks. Indeed, you will soon learn that QFT cannot be learnt out of just one book! Maggiore's book is a remarkably well crafted selection of topics that will lead everybody to see the whole structure of a quantum field theory, all the way up to non-abelian gauge theories, in a very compact and efficient way. It is a modern approach in the way it connects among different domains, whenever possible, and builds some very solid foundations for all students to be able to apply QFT concepts to a variety of problems. It also provides a superb introduction for those students who will follow up with the second part of this course, QFT B (PHY 5669). On the other hand, Peskin and Schroeder's book has more details and more advanced topics, and will be one of our main references in QFT B. Hence, I think it can be beneficial to most of you to read through it during this class, or to study it in depth if you are interested in continuing studying QFT. Topics wise, we will follow the outline of Maggiore's book. One nice feature of the book is that it spends some time at the beginning introducing the fundamental mathematical structures (Lie groups, Lorentz and Poincar\'e symmetries) that makes the construction of a quantum field theory more natural and less arbitrary. We will then discuss the application of these principles to the construction of classical field theories and then introduce the quantization of both free and interacting fields. With this background, we will be able to study Quantum Electrodynamics (QED), as the prototype example of abelian gauge theories, and calculate some of its most remarkable predictions. If time allows, I would like to at least have a glance at non-abelian gauge theories, with excursions in either Quantum Chromodynamics (QCD) or the theory of electroweak interactions (Standard Model), which will be further developed in QFT 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
08/25 Syllabus. Introduction to QFT. Natural Units. [MM] (Ch.1), [SW](Ch.1)
08/27 Classical systems of fields: Lagrangian and Hamiltonian formalism. [MM] (Sec. 3.1), [Gol](Ch. 11), [PS](Sec. 2.2)
09/01 Brief introduction to properties of Lie Groups. Review of the Lorentz Group. [MM](Sec. 2.1-2.2), your notes
09/03 Representations of the Lorentz Algebra. [MM](Sec. 2.3-2.4), your notes
09/08 Classification of fields: scalar, spinor, and vector fields as different representations of the Lorentz Algebra. [MM](Sec. 2.4-2.6), your notes
09/10 Noether's theorem in classical field theory. [MM](Sec. 2.7), [PS](Sec. 2.2), [BS], Notes
09/15 Lagrangian for a classical real scalar field, Klein-Gordon equation, energy and momentum of a system of classical real scalar fields. [MM](Sec. 3.3), [PS] (Sec. 2.3)
09/17 Klein-Gordon quantum field: quantization, construction of physical states. Spin-statistics theorem. [MM](Sec. 4.1), [PS] (Sec. 2.3)
09/22 Klein-Gordon quantum field: the Feynman propagator. Case of a complex scalar field. [MM] (Secs. 5.4, 3.3.2, 4.1.2), [PS] (Sec. 2.4), your notes.
09/24 Introduction to spinor fields: Weyl spinors/equation, properties of the classical fields. [MM] (Secs. 3.4.1), [PS] (Sec. 3.2), your notes.
09/29 Introduction to spinor fields: Dirac and Majorana spinors, Dirac equation, Dirac Lagrangian and its symmetries. [MM] (Secs. 3.4.2-3.4.4), [PS] (Sec. 3.2), your notes.
10/01 Classical solutions of the Dirac equation, detailed calculation and discussion of the results. [MM] (Secs. 3.4.2), [PS] (Sec. 3.3), your notes.
10/06 Quantization of Dirac fields, construction of physical states. Spin-statistics relation. [MM] (Sec. 4.2), [PS] (Sec. 3.5)
10/08 The electromagnetic field: classical theory. [MM] (Sec. 3.5)
10/13 Quantization of the electromagnetic field: quantization in radiation gauge vs covariant quantization. [MM] (Sec. 4.3)
10/15 Introduction to theories of interacting fields. [MM](Sec. 5.1-5.2), [PS] (Secs. 4.1)
10/20 Interaction representation, time-evolution operator. Setting up the perturbative expansion of correlation functions. [MM](Sec. 5.3), [PS] (Secs. 4.2)
10/22 The S matrix. S matrix element and the LSZ reduction formula. [MM](Sec. 5.1-5.2), [PS] (Secs. 4.5)
10/27 The LSZ reduction formula (completing the discussion). Perturbative expansion of correlation functions. [MM](Sec. 5.3-5.4), [PS] (Secs. 4.2-4.3)
10/29 Interacting fields: Wick theorem, introduction to Feynman diagrams. [MM] (Sec. 5.5), [PS](Secs. 4.3-4.4)
11/3 NO CLASS.
11/5 NO CLASS. Homework will be due next Tuesday.
11/10 Interacting fields: correlation functions as sum of connected Feynman diagrams. [PS](Sec. 4.4)
11/12 Computing S-matrix elements from Feynman diagrams. [MM] (Sec. 5.5.1), [PS](Secs. 4.6)
11/13 MAKE-UP CLASS: 12:30 p.m. Keen 707. Cross section for a 2->n scattering process (scalar fields). [MM](Sec. 6.2-6.4), [PS](Sec. 4.5 and 7.2)
11/17 Introduction to QED and to the general idea of local invariance. QED Feynman rules. [MM] (Sec. 7.1), [PS](Secs. 4.8 and 15.1)
11/18 MAKE-UP CLASS: 12:00 p.m. Keen 707. QED: detailed calculation of the tree level cross section for (e+ e- -> mu+ mu-) [MM] (Sec. 7.3, Prob. 7.1), [PS] (Sec. 5.1)
11/19 Introduction to loop divergences: scalar phi^4 theory, two- and four-point functions, UV divergences and their regularization. [MM] (Sec. 5.5.2), [PS](Ch. 7 and Sec. 10.2)
11/24 Introduction to the renormalization of the scalar phi^4 theory: field and mass renormalization. [MM] (Secs. 5.5.2 and 5.6), [PS](Ch. 10)
12/01 Introduction to the renormalization of the scalar phi^4 theory: coupling renormalization. Brief introduction to dimensional regularization. [MM] (Secs. 5.5.2 and 5.6), [PS](Ch. 10)
12/03 Systematic approach to the renormalization of a generic field theory with special emphasis on a phi^n theory, QED, and a Yukawa-type theory. [MM] (Secs. 5.6 and 7.2), [PS](Ch. 10, with some elements of Ch. 7)

[MM],[PS],[SW], [Sr], [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 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 a 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.

Laura Reina
Last modified: Tue Dec 4 13:54:45 EST 2007