PHY 5667 : Quantum Field Theory A

Lectures: 11:00-12:15, Tuesday and Thursday, in UPL 107.

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

Topics:

We will cover the first seven chapters of the textbook. This will allow us to introduce the classical and quantum theory of fields, the role of global and local (or gauge) symmetries, and to discuss in detail the case of Quantum Electrodynamics (QED), one of the most successful theories of modern and contemporary Physics. We will explicitly show the renormalizability of the theory, and calculate several physical observables thoroughly. This will set the basis for further developments 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
08/29 Syllabus. Introduction to QFT and QED. [SW](Ch.1), [Scw]
08/31 QUALIFYING EXAM: CLASS CANCELLED.
09/05 Classical systems of fields: Lagrangian and Hamiltonian formalism. Noether's theorem. [Gol] (Ch. 11), [Text](Sec. 2.2), [Ry](Sec. 3.1-3.2), [BS]
09/07 Energy-momentum tensor. Angular momentum tensor. Brief review of Lorentz transformations. [Text](Sec. 3.1), [SW](Secs.2.3,2.4,5.6)
09/12 Klein-Gordon quantum field: quantization of a system of real scalar fields, annihilation and creation operators. Comments on generalization to the case of a complex scalar field. [Text](Sec. 2.3)
09/14 Klein-Gordon quantum field: Hamiltonian and momentum operators, number density operator, physical spectrum. Time evolution of field operators: Heisemberg representation. [Text](Secs. 2.3-2.4)
09/19 Klein-Gordon quantum field: Feynman propagator, detailed discussion. Some comments on the current homework. [Text](Sec. 2.4)
09/21 Study of the spinor representation of the Lorentz Group. Dirac equation. [Text](Sec. 3.2)
09/22 Properties of gamma matrices. Dirac bilinears. Dirac Lagrangian. [Text](Secs. 3.2,3.4)
09/26 Vector and axial currents. Study of the solutions of the Dirac equation (to be continued). [Text](Sec. 3.3)
09/28 Study of the solutions of the Dirac equation. Properties of u and v spinors. [Text](Sec. 3.3)
10/03 Quantization of the Dirac field. [Text](Sec. 3.5)
10/05 Quantization of the Dirac field: spin operators, spin quantum number of physical states. Dirac field propagator. [Text](Sec. 3.5)
10/10 Qualitative discussion of the quantization of vector fields. `[Text](part of Secs. 4.8 and 5.5)
10/12 Introduction to theories of interacting fields. [Text](Sec. 4.1)
10/17 Interacting fields: perturbative expansion of correlation functions. [Text](Sec. 4.2)
10/19 Interacting fields: Wick theorem, introduction to Feynman diagrams. [Text](Secs. 4.3-4.4)
10/24 Interacting fields: correlation functions as sum of connected Feynman diagrams (Part I). [Text](Sec. 4.4)
10/26 Interacting fields: correlation functions as sum of connected Feynman diagrams (Part II). [Text](Sec. 4.4)
10/31 Interacting fields: cross section for a 2->n scattering process (scalar fields). [Text](Sec. 4.5, read also results in Sec. 7.2)
11/2 Interacting fields: computing S-matrix elements from Feynman Diagrams. [Text](Sec. 4.6)
11/07 Interacting fields: Feynman Rules for scalar fields and fermion fields. Calculation of ff->ff scattering in Yukawa theory. [Text](Secs. 4.6-4.7)
11/09 QED: Feynman rules, detailed calculation of the tree level cross section for (e+ e- -> mu+ mu-) [Text](Sec. 5.1)
11/14 QED: more about (e+ e- -> mu+ mu-) and its physical relevance; helicity amplitudes for (e+ e- -> mu+ mu-). Crossing symmetry (e- mu- -> e- mu- scattering). [Text](Secs. 5.1, 5.2, and 5.4)
11/16 QED: Compton scattering, Klein-Nishina formula. Introduction to radiative corrections in QED. Example: calculation of the cross section for electron scattering including the complete first order QED virtual and real corrections. Problem: UV and IR divergences. [Text](Secs. 5.5) and 6.1
11/21 QED: calculation of the O(alpha) real corrections to electron scattering. Extraction of soft IR divergences. [Text](Secs. 6.1 and your notes)
11/28 QED: the electron-photon vertex (Feynman parametrization, momentum integrals). [Text](Sec. 6.3)
11/30 QED: the electron-photon vertex (Pauli-Villars regularization, UV singularities). [Text](Sec. 6.3)
12/5 QED: the electron-photon vertex (IR singularities). The electron self-energy: Field strength and mass renormalization. Cancellation of UV and IR singularities in the electron scattering cross section at O(alpha). [Text](Sec. 6.4 and your notes. Secs. 7.1-7.2)
12/7 The photon self-energy and its relation to the QED coupling renormalization: the one-loop corrections. Summary of the results obtained and explicit discussion of the renormalization of the UV divergences (fields, mass, and charge renormalization), at one-loop (explicit) and in general (starting from the QED Lagrangian). [Text](Sec. 7.5 (parts of), Sec. 7.2 (end of), Sec. 10.3 and your notes)

[Text],[IZ],[SW],[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: 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 is a take-home exam. You will get it a couple of weeks before the end of the semester and will have till Thursday December, 14 at 12:00 pm to return it to me.

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 17:04:09 EST 2007