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
01/08 Review of the sytematic of QED renormalization. [MS] (Ch. 16-19), [PS] (Sec. 10.3)
01/10 NO CLASS. Work on this warm-up project, the discussion of which can now be found here.
01/15 Calculating the O(alpha) corrections to the e^+ e^- -> mu^+ mu^- cross section: review of UV divergences (and their renormalization) and detailed discussion of IR divergences. Extracting IR singularities from virtual corrections: case of vertex corrections. [MS] (Ch. 20), [PS] (Sec. 6.4). Also, look at the discussion of the warm-up project.
01/17 Calculating the O(alpha) corrections to the e^+ e^- -> mu^+ mu^- cross section: IR divergences from real-photon emission. Cancellation of IR divergences betweeen virtual and real corrections. Interpretation of initial-state and final-state IR divergences in QED and beyond. [MS] (Ch. 20). Here is a useful reference. Also, look at the discussion of the warm-up project.
01/22 Introduction to non-renormalizable theories and their predictivity. [MS] (Ch. 21.2)
01/24 Non-renormalizable theories: bottom-up and top-down approach. The case of the Fermi interaction. [MS] (Ch. 22.2)
01/29 Introduction to the renormalization group: continuum approach, first examples of RG equations, definition of beta-function and mass anomalous dimension. [MS] (Ch. 23), Class Notes.
01/31 Calculation of the beta-function of QED, and of the running coupling (using dimensional regularization and MSbar subtraction). Comparison of different renormalization schemes vis-a-vis the resummation of large logarithmic corrections via RG evolution. [MS] (Ch.23.2), Class Notes.
02/05 Calculation of the mass anomalous dimension in QED, and of the running mass (using dimensional regularization and MSbar subtraction). Discussion of the calculation of the beta function, and mass anomalous dimension: relation to single poles of the coupling and mass renormalization constants. [MS] (Ch.23.5), Class Notes.
02/07 Anomalous dimension of composite operators: Lagrangian and external operators. RGE for EFT operators and Wilson coefficients. Importance of RG improved EFT and their applications. [MS] (Ch.23.4), plus some lecture notes from class. You may enjoy these very nice recent series of lectures on Renormalization and EFT and EFT: where scales become separated . Here are my HEP2 lecture notes on introduction to EFT: Lesson-1, Lesson-2, Lesson-3, Lesson-4, Lesson-5.
02/12 Introduction to path-integral quantization. [MS] Sections 14.1-14.2, [PS] Section 9.1. [Sr] Chapter 6-7.
02/14 Path-integral methods in quantum field theory: generating functional and correlation functions. [MS] Sections 14.2-14.3, [PS] Section 9.2, [Sr] Chapter 8.
02/19 Path-integral and generating functional of interacting theories. Your notes. [Sr] Chapter 9.
02/21 Path Integral quantization for spinor fields. [PS] Sec. 9.5, [Sr] Chapter 43.
02/26 Path Integral quantization of the electromagnetic field, Faddeev-Popov method. [PS] Sec. 9.4, [Sr] Chapter 57.
02/28 Path integral and symmetries in quantum field theory. Ward-Takahashi identities in QED. [PS] Sec. 9.6.
03/05 Wilsonian approach to renormalization and renormalization group theory. [MS] Section 23.6, [PS] Section 12.1, WK-paper
03/07 Non-abelian gauge theories: introduction. [MS] Chapter 25, [PS] Sections 15.1-15.2 (Section 15.3: read as reference)
03/12 Quantum non-abelian gauge theories: Faddeev-Popov method, ghost fields, Feynman rules. [MS] Chapetr 25, [PS] Sections 15.2 and 16.1
03/14 Quantum non-abelian gauge theories: renormalization and one-loop structure. Beta function and running coupling: asymptotic freedom and confinement. [MS] Chapter 26 (specialized to QCD), [PS] Sections 16.2, 16.5, and 16.7.
03/19 Spring Break
03/21 Spring Break
03/26 Global symmetries of abelian and non-abelian gauge theories. BRST invariance. [MS] Sections 25.3 and 25.4.2
03/28 Deep Inelastic Scattering: from experiments to the parton model. Bjorken scaling. [MS] Section 32.1.3, [PS] Ch. 14 and Section 17.3
04/02 Deep Inelastic Scattering: interpretation in terms of a non-abelian gauge theory, namely QCD. The idea of parton densities and their universality in describing hadronic scattering processes. [MS] Section 32.1.3, [PS] Sections 16.7 and 17.4
04/04 Parton evolution: a QED toy-model. [PS] Section 17.5
04/09 Parton evolution: the Altarelli-Parisi equations. Calculating hadronic scattering processes in QCD. [MS] Section 32.2, [PS] Section 17.5
04/11 Spontaneous Symmetry Breaking: the case of global symmetries. Discrete symmetry case. [MS] Section 28.1, [PS] Section 11.1, your notes.
04/12 Make-up class: 8:45-10:00 AM, 701 Keen.
Spontaneous Symmetry Breaking: the case of continuous global symmetries. Goldstone theorem.		 [MS] Section 28.2, [PS] Section 11.1, your notes.
04/16 Global symmetries of the QCD Lagrangian in the chiral limit: pions as pseudo-Goldstone bosons. Gauge theories with spontaneous symmetry breaking, abelian case. [MS] Sections 28.2 and 28.3, [PS] Sectons 19.3 and 20.1 (look also at Section 11.1).
04/18 Gauge theories with spontaneous symmetry breaking, non-abelian case. A useful example: detailed discussion of SU(2) case. [MS] Section 28.3, [PS] Section 20.1
04/19 Make-up class: 8:45-10:00 AM, 701 Keen.
The Glashow-Weinberg-Salam theory or Standard Model: SSB and electroweak interactions, gauge boson mass eigenstates, electroweak currents. 		[MS] Chapter 29, [PS] Section 20.2
04/23 NO CLASS
04/25 NO CLASS

[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 Exam is now available and will have to be turned in by Friday, May 3rd, 2018 at the latest.

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