PHY 5669 : Quantum Field Theory B


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


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:

Topics:

In QFT A you have learned the language and basic tools of Quantum Field Theory and you have seen a masterpiece realization of the formalism in the theory of Quantum Electrodynamics (QED). Strong of that, in QFT B we will aim at introducing a much broader set of theories known as Non-Abelian Gauge Theories (remember, QED is an abelian gauge theory). They are the theories, like Quantum Chromodynamics (QCD) or the theory of Electroweak Interactions, that describe the dynamics of elementary particles over a very broad range of energies, from the high-energies of collider physics and astrophysics phenomena to some regimes of nuclear physics phenomena. Because of the fundamental role played by symmetries, the topics covered in QFT B are more naturally developed using the path integral quantization method, which we will introduce in the first lectures. We will then move to a systematic discussion of the renormalization of a generic field theory and study the renormalization group associated to it, which will bring out the true nature and meaning of the procedure of renormalization. The formalism of path integral will also allow us to efficiently develop the quantization of non-abelian gauge theories and their properties. After a general introduction, we will focus on the structure and properties 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
01/09 Introduction to path-integral quantization. [PS] Section 9.1. [Sr] Chapter 6-7.
01/11 NO CLASS We will make up adding time to (previous) and following classes.
01/16 CLASS WILL BE in ROOM 503.
Path-integral methods in quantum field theory: correlation functions in terms of functional integrals.
[PS] Section 9.2, [Sr] Chapter 8.
01/18 Path-integral methods in quantum field theory: generating functional and correlation functions. [PS] Section 9.2, [Sr] Chapter 8.
01/23 Path Integral Methods in quantum field theory: quantization of the electromagnetic field, Faddeev-Popov method. [Text] Sec. 9.4, [Sr] Chapter 57.
01/25 CLASS WILL BE in ROOM 503.
Path Integral Methods in quantum field theory: quantization of spinor fields; QED.
[Text] Sec. 9.5, [Sr] Chapter 43.
01/30 Questions and answers about previous lessons and homework. Your notes.
02/01 CLASS WILL BE in ROOM 503.
Path integral and symmetries in quantum field theory. Ward-Takahashi identities in QED.
[Text] Sec. 9.6.
02/06 Non-abelian gauge theories: introduction. [PS] Sections 15.1-15.2 (Section 15.3: read as reference)
02/08 Non-abelian gauge theories: the Yang-Mills Lagrangian. [PS] Sections 15.2 and 16.1
02/13 Quantum non-abelian gauge theories: Faddeev-Popov method, ghost fields, one-loop structure.[PS] Sections 16.2 and 16.5
02/15 Quantum non-abelian gauge theories: ghost fields and unitarity.[PS] Sections 16.1 and 16.3
02/20 Renormalization group: puzzling experimental facts and new theoretical ideas converging towards the idea of rescaling of couplings (and masses) in a Lagrangian. Your notes
02/22 Renormalization group: Callan-Symanzik equation, definition of beta-function, mass anomalous dimension, and field anomalous dimension. [PS] Section 12.2, [Sr] Chapter 27.
02/27 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.
03/01 Renormalization group: calculation of the beta function of abelian/non-abelian gauge theories: QED vs QCD. [PS] Sections 12.3 and 16.7, your notes
03/06 Renormalization group: effective coupling constant, expansion in leading logarithms. Your notes.
03/08 CLASS WILL BE in ROOM 503.
Renormalization group: Wilson approach to renormalization theory.
[PS] Section 12.1, WK-paper
03/13 Spring Break
03/15 Spring Break
03/20 NO CLASS
03/22 NO CLASS
03/27 NO CLASS
03/29 NO CLASS
03/30 Make-up class: 10:00-11:30 AM, 701 Keen.
Deep Inelastic Scattering: from experiments to the parton model. Bjorken scaling.
[PS] Ch. 14 and Section 17.3
03/30 Make-up class: 5:00-6: PM, 701 Keen.
Deep Inelastic Scattering: derivation of parton distribution functions.
[PS] Section 17.5
04/03 Parton evolution: a QED toy-model. [PS] Section 17.5
04/05 Parton evolution: the Altarelli-Parisi equations. Calculating hadronic scattering processes in QCD. [PS] Section 17.5
04/06 Make-up class: 10:00-11:30 AM, 701 Keen.
Spontaneous Symmetry Breaking: the case of global symmetries. Discrete symmetry case.
[PS] Section 11.1, your notes.
04/10 Spontaneous Symmetry Breaking: the case of continuous global symmetries. Goldstone theorem. [PS] Section 11.1, your notes.
04/12 Global symmetries of the QCD Lagrangian. [PS] Section 17.1, your notes.
04/13 Make-up class: 10:00-11:30 AM, 701 Keen.
Global symmetries of the QCD Lagrangian in the chiral limit: pions as pseudo-Goldstone bosons.
[PS] Section 19.3, your notes.
04/17 Gauge theories with spontaneous symmetry breaking, abelian case. [PS] Section 20.1. Look also at Section 11.1.
04/19 Gauge theories with spontaneous symmetry breaking, non-abelian case. A useful example: detailed discussion of SU(2) case. [PS] Section 20.1
04/24 The Glashow-Weinberg-Salam theory or Standard Model: SSB and electroweak interactions, gauge boson mass eigenstates, electroweak currents. [PS] Section 20.2
04/26 The Glashow-Weinberg-Salam theory or Standard Model: fermion masses, flavor mixing, and the origin of CP-violation. Highlights of the quantization of gauge theories with SSB. [PS] Sections 20.2, 20.3, and 21.1.
SM-Lecture-1, SM-Lecture-2, SM-Lecture-3, SM-Lecture-4

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

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 50% on the homework and 50% on the Final Project, 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 Project is now available and will have to be turned in by Friday, May 4th, 2018 at the latest. In the following you will find links to a couple of references that can help you while you work at your final project. The first reference in particular contains a nice introductory section on the Standard Model (SM) Lagrangian, and a complete set of consistent SM Feynman rules for a given gauge choice. It also discusses several important aspects of loop calculations in the SM that you do not need for your project, but can be useful to you in the future. The second reference is more specific to a particular Higgs-boson decay process, and you will figure out how to use it.


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: Thu Jan 4 13:54:45 EST 2017