Quantum Field Theory 2
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README.md

Quantum Field Theory 2

PHYS 7326, Spring 2018

Instructor: Professor Jim Halverson

E-mail: j.halverson@northeastern.edu

Phone: 617-373-2957

Office Hours: M 8:00-9:30, 11:45-1:15

Grader: Amin Abou Ibrahim, abouibrahim.a@husky.neu.edu

Course Information

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.

Course Material

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
    • Superfields
    • 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.