Quantum Field Theory II
Physics 8808.02, Spring 2013
Instructor: Yuri
Kovchegov
Office: M2042 Physics Research Bldg
Office Hours: stop by anytime
Course Meets: Tuesdays, Thursdays 11:10 am - 12:30 pm, Denney Hall, room 0207.
Grader: Douglas Wertepny , PRB M2041
*** First Class Meets January 10, 2013 -- I am out of town on January 8, 2013 ***
*** There will be no class Thursday, January 31, 2013 -- I will be out of town ***
*** There will be no class Tuesday, April 16, 2013 -- I will be out of town ***
Brief Syllabus (for both semesters):
- Autumn Semester: we will learn how to treat fields (not particles!), such as electric and magnetic fields from the E&M class, as quantum-mechnical objects (how to "quantize" them). We will study the most important language of quantum field theory (and arguably of all of modern physics) - the language of Feynman diagrams. We will use Feynman rules to calculate cross sections for some (lowest order in the coupling constant) scattering processes. Formal topics are:
- Classical field theory
- Lorentz and Poincare groups and classification of fields
- Canonical quantization of free scalar, Dirac and electromagnetic fields
- Correlators in free field theory, Feynman propagator
- Interacting fields and Feynman diagrams
- Cross sections, S-matrix, and the LSZ reduction formula
- Quantum Electrodynamics (QED): cross section calculations for tree-level processes
- Spring Semester: we will find out that the Feynman diagrams at the higher (loop) orders in the coupling often lead to bad infinities. We will learn how to regulate the infinities (make them finite) and how to do them away altogether using the process or renormalization. We will then learn how to quantize the fields using Feynman's functional integrals, which is a beatiful alternative to canonical quantization. After that we will cover non-Abelian gauge theories, which are the backbone of the Standard Model of Particle Physics, as they explain both the strong and the electroweak interactions. We will study the theory of strong interactions - quantum chromodynamics (QCD). In the process we will have another scare as we will discover another sick infinity, the so-called Landau pole, and will learn why Landau did not believe in field theories. We will see why Landau's worries were wrong for QCD, but probably right for QED. We will then explore some special topics in Quantum Field Theory, several of which are listed below. Topics will be:
- Radiative corrections, dimensional and Pauli-Villars regularizations, Ward identity
- Renormalization group, renormalization of QED and scalar theories, running coupling constant
- Functional integration
- Non-Abelian gauge theories, Faddeev-Popov ghosts
- Quantum Chromodynamics (QCD): asymptotic freedom and Landau pole, e^+e^- annihilation, Deep Inelastic Scattering (DIS) and parton model
- Some special topics on demand: possibly quantum anomalies, instantons and other topological objects in field theory, DGLAP evolution, small-x physics and parton saturation, Electroweak theory, Higgs mechanism - the choice is up to you
Textbook:
Recommended Reading :
Here's a list of books to complement Peskin and Schroeder. The books are listed in the order of
increasing difficulty (more or less).
An excellent source on Group theory for particle and nuclear physicists:
Lecture Notes:
These are the notes from when I taught this class last academic year, they may be updated as we go through the course.
- Quantum Electrodynamics (QED): Tree-Level Processes (continued from last semester)
- Regularization and Renormalization
- Functional Integral Quantization
- Non-Abelian Gauge Theories
Homework Assignments:
Homeworks are due at 5 pm on the due date. Please put them in either my or the grader's mailboxes in PRB or give them to me in class or give them to the grader in his office, which is directly across from mine (or slide them under my office door if other options are not available). (Solutions are password protected, they are for the use of OSU students and faculty only: if you are an OSU student or a faculty member and are interested in accessing them please write to me.)
Grading will be based on the HW's.
Yuri Kovchegov