Quantum Field Theory 2
PHYS 7326, Spring 2018
Instructor: Professor Jim Halverson
Office Hours: M 8:00-9:30, 11:45-1:15
Grader: Amin Abou Ibrahim, firstname.lastname@example.org
Course Schedule: Lectures M 10:00-11:40, R 1:30-3:10
Course Location: Churchill 321
Description: The goal of this course is for you to learn second and third semester topics in quantum field theory. We will cover non-abelian gauge theory, more condensed matter applications, supersymmetry, and conformal field theory.
Preparation: A strong and broad background in quantum field theory is necessary. See here.
Resources: The primary textbook for this course is:
- Quantum Field Theory and the Standard Model, M. Schwartz.
I will again lecture from my notes, which draw from a number of sources. The sources for each section of the course are listed under course material. Collectively, they are:
- Quantum Field Theory in a Nutshell (2nd Ed.), A. Zee.
- Condensed Matter Field Theory, A. Altland and B. Simons
- Supersymmetry and Supergravity, J. Wess and J. Bagger
- An Introduction to Quantum Field Theory, M. Peskin and D. Schroeder.
- Applied Conformal Field Theory, by Paul Ginsparg.
- A supersymmetry primer, by Stephen Martin.
Homework and Exams: There will be biweekly homework assignments designed to help guide you through the material. There will be a take home midterm and final exam, each of which will involve one or more classic computations in quantum field theory. There will also be an in-class midterm. Homework may be a joint effort, but the exams must be your work and yours alone. The texts above may be used on exams.
Late homework policy: Illness and other things come up sometimes, so homework may be turned in within 10 days of the due date, but with a 25% penalty. However, it is strongly recommended to not get behind on the class material in order to complete a past due homework.
Academic Integrity: Be sure to review Northeastern Academic Integrity policies, which are here.
Grading: 20% homework, 40% midterm (20% in class, 20% take home), 40% final exam.
Topics are organized according to order of presentation. I had originally imagined beginning with condensed matter for the sake of fluidity with last semester, but some aspects of non-abelian gauge theory may be important there.
Topic 1: Non-abelian Gauge Theory
We will work primarily from my notes and Schwartz.
- Group Theory
- Yang-Mills Theory
- Gauge Fixing and Fadeev-Popov
- Feynman Rules
- Physical States and BRST Cohomology
- Asymptotic Freedom of Yang-Mills and QCD
- Gauge Anomalies
Topic 2: More Condensed Matter
We will work primarily from Zee and Peskin-Schroeder.
- Fermions in arbitrary dimensions
- Topological Defects (Instantons)
- Non-linear sigma model, (anti) ferromagnetism, and asymptotic freedom
- Chern-Simons theory
- Particle-vortex duality
Topic 3: Supersymmetry
We will work primarily from Wess-Bagger and Martin.
- Two component spinors and identities
- SUSY algebra and representations
- Component fields
- Chiral Superfields
- Vector Superfields
- Gauge Invariant Interactions
- Spontaneous Symmetry Breaking
- Minimal Supersymmetric Standard Model and SUSY Phenomenology
Topic 4: Conformal Field Theory
We will work primarily from Ginsparg.
- Conformal theories in d-dimensions
- Conformal theories in 2 dimensions
- Central Charge and Virasoro Algebra
Comments and Recommendations
- Each topic in the course will begin with a brief discussion of the central ideas and why they are important.
- Since this material can be quite dense with formalism, each lecture will begin with a concrete outline and an explanation of the basic logic behind the physics presented in the lecture.
- During lecture, please ask questions! An interactive classroom will be beneficial to all.
- We will cover a lot of material, and it is important to not get behind.