PHY 5667 : Quantum Field Theory A

Lectures: 11:00-12:15, Tuesday and Thursday, Keen 701.

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

Textbook and suggested references:

Textbooks used in the past: 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: An excellent reference for Group Theory:

Topics:

Quantum field theory (QFT) is fundamental to understanding contemporary theoretical physics and its evolution over the last several decades. In this class we will introduce the classical and quantum theory of fields, the role of global and local (or gauge) symmetries, the application of QFT to the calculation of scattering amplitudes. We will discuss in detail the case of Quantum Electrodynamics (QED), including its renormalizability, and calculate several physical observables thoroughly, emphasizing those aspects that made of QED one the most successful theories of modern physics. This will set the background 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
08/28 Introduction to QFT. Classical systems of fields: Lagrangian and Hamiltonian formalism. [MS](Ch.1 and 3), [PS](Ch.1), [SW](Ch.1)
08/30 Lagrangian for a classical real scalar field, Klein-Gordon equation. Lorentz transformations (quick review, more to come). [MS](Ch. 3), [PS](Sec. 2.2), [MM] Chapter 2
09/04 More on Lorentz transformations and Lorentz invariance in QFT. [MM] Chapter 2
09/06 Noether's theorem in classical field theory. Energy-momentum and angular-momentum tensors for a system of fields. [MS] (Sec. 3.3), [PS] (Sec. 2.2), [BS]
09/11 NO CLASS
09/13 NO CLASS
09/18 Quantization of a system of scalar fields: Klein-Gordon quantum field. [MS] (Sec. 2.3), [PS] (Sec. 2.3-2.4), [MM] (Sec. 4.1)
09/20 Klein-Gordon quantum field: quantization, Hamiltonian and momentum operators, number density operator. [PS] (Sec. 2.3), [MM](Sec. 4.1)
09/21 Make-up class, 8:30-9:45 a.m., Keen 701.
Klein-Gordon quantum field: construction of physical states and their interpretation. 		[MS] (Sec. 2.3), [PS] (Secs. 2.3-2.4), [MM] (Secs. 3.3.2, 4.1.2)
10/25 Klein-Gordon quantum field: Feynman propagator. [MS] (Sec. 6.2), [PS](Secs. 2.4), [MM] (Sec. 5.4)
10/27 The S matrix. S-matrix elements and the LSZ reduction formula. [MS] (Sec. 6.1), [PS] (Secs. 4.5), [MM] (Sec. 5.1-5.2)
09/28 Make-up class, 8:30-9:45 a.m., Keen 701
Introduction to theories of interacting fields. Towards a perturbative expansion of correlation functions.		 [MS] (Sec. 7.2), [PS] (Secs. 4.1 and 4.2), [MM] (Secs. 5.3)
10/02 Interacting fields: Perturbative expansion of correlation functions. [MS] (Secs. 7.2, 7.A), [PS] (Secs. 4.2), [MM] (Secs. 5.3)
10/04 Wick's theorem, introduction to Feynman diagrams. [MS] (Secs. 7.3, 7.A) [PS] (Secs. 4.3-4.4), [MM] (Sec. 5.5)
10/09 CLASS CANCELED due to weather conditions
10/11 CLASS CANCELED due to weather conditions
10/16 Correlation functions as sum of connected Feynman diagrams. [MS] (Sec. 7.2), [PS] (Sec. 4.4)
10/18 Computing S-matrix elements from Feynman diagrams. [MS] (Ch. 6, Sec. 7.3), [PS] (Secs. 4.6), [MM] (Sec. 5.5.1)
10/19 Make-up class, 8:30-9:45 a.m., Keen 701
Cross section for a 2->n scattering process (scalar fields).		 [MS] (Ch. 5, Sec. 7.4), [PS] (Sec. 4.5 and 7.2), [MM] (Sec. 6.2-6.4)
10/23 Lorentz Group and its representations. Classification of fields: scalar, spinor, and vector fields as different representations of the Lorentz Algebra. [MS] (Secs. 10.1-10.2), [PS](Secs. 3.1), [MM](Sec. 2.4-2.6), [SW](Sec.2.3,2.4,5.6)
10/25 Introduction to spinor fields: Weyl spinors (Lagrangian, equation). [MS] (Sec. 10.2), [PS] (Sec. 3.2), [MM] (Secs. 3.4.1-3.4.4).
11/26 Make-up class, 8:30-9:45 a.m., Keen 701
Introduction to spinor fields: Dirac spinors, Dirac Lagrangian, Dirac equation. 		[MS] (Sec. 10.2), [PS] (Sec. 3.2), [MM] (Secs. 3.4.1-3.4.4).
10/30 Introduction to spinor fields: symmetries of the Dirac Lagrangian. [MS] (Secs. 8.2-8.3), [PS] (Sec. 3.2), [MM] (Secs. 3.4.1-3.4.4).
11/01 Classical solutions of the Dirac equation, detailed calculation and discussion of the results. [MS] (Sec. 11.1-11.2), [PS] (Sec. 3.3), [MM] (Secs. 3.4.2).
11/06 Quantization of Dirac fields, construction of physical states. Spin-statistics relation. [MS] (Secs. 12.1-12.3), [PS] (Sec. 3.5), [MM] (Sec. 4.2)
11/08 Fermion Feynman rules. Example: Yukawa Theory. [MS] (Secs. 13.1), [PS] (Secs. 4.7-4.8)
11/13 Quantization of the electromagnetic field: briefly about covariant quantization. [MS] (Secs. 8.2, 8.4-8.5), [PS] (Secs. 4.1, 4.8), [MM] (Sec. 4.3)
11/15 Introducing the Lagrangian of QED and scalar QED. QED Lagrangian from gauge symmetry principle. QED Feynman rules. [MS] (Secs. 8.3, 9.1-9.2, 13.1-13.2) , [PS] (Secs. 4.1, 4.8), [MM] (Secs. 7.1, 7.3)
11/20 Calculation of tree level cross sections in QED. Examples: e+ e- -> mu+ mu-. [MS] (Secs. 9.3, 13.3), [PS] (Secs. 5.1, 5.3), [MM] (Secs. 7.1, 7.3)
11/27 Introduction to radiative corrections in QED. Cross section for e+ e- -> mu+ mu- beyond the tree level: O(alpha) virtual and real corrections. UV and IR divergences, origin and general treatement. Your notes, [PS] (Introduction to Chapter 6)
11/29 Systematic of renormalization: determining the UV divergent n-point correlation functions of a given QFT. The case of QED: photon and electron self-energies and electron-photon interaction. Your notes, [PS] (Sec. 10.1)
12/04 The photon self-energy: detailed calculation of the one-loop correction. Feynman parametrization of loop integrals. Loop-momentum integration. Dimensional regularization. [MS] (Ch. 16), [PS] (Sec. 7.5, and parts of Sec. 6.3)
12/06 QED renormalization: expressing physical observables in terms of other physical observables (electron mass and charge)! Systematic implementation at the Lagrangian level through counterterm vertices. [MS] (Chs. 17-19, you do not need everything, but reading through them will be very beneficial), [PS] (Parts of Secs. 6.2 and 7.2, and Sec. 10.3)

[MS], [PS], [MM], [SW], [Sr], [Scw], [IZ], [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 10:00 p.m. to 12:00 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 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: Wed Aug 22 7:51:54 EST 2018