Related papers: Integrble Models in Condensed Matter Physics
We review applications of the sine-Gordon model, the O(3) non-linear sigma model, the U(1) Thirring model, and the O(N) Gross--Neveu model to quasi one-dimensional quantum magnets, Mott insulators, and carbon nanotubes. We focus upon the…
In these lecture notes, I review the ``linear sigma model" approach to (0,2) string vacua. My aim is to provide the reader with a toolkit for studying a very broad class of (0,2) superconformal field theories with the requisite properties…
We review some links between Lie-theoretic polytopes and field theories in physics, which were proposed in the 1990's. A basic ingredient is the Coxeter Plane, whose relation to integrable systems and the Stokes Phenomenon has only recently…
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
This script is based on the notes the author prepared to give a set of six lectures at the Les Houches School "Integrability in Atomic and Condensed Matter Physics" in the summer of 2018. The school had its focus on the application of…
These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students,…
These notes briefly summarize the lectures for the Summer School "Optimal transportation: Theory and applications" held by the second author in Grenoble during the week of June 22-26, 2009. Their goal is to describe some recent results on…
We reformulate the self-dual Einstein equation as a trio of differential form equations for simple two-forms. Using them, we can quickly show the equivalence of the theory and 2D sigma models valued in an infinite-dimensional group, which…
The AdS/CFT correspondence provides quantum theories of gravity in which spacetime and gravitational physics emerge from ordinary non-gravitational quantum systems with many degrees of freedom. Recent work in this context has uncovered…
These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular…
I study how to apply relativistic quantum field theory to condensed matter systems. The motivation for this is examined and then two separate elements are considered. First we identify the precise relationship between relativistic and…
Lectures note for Cargese 99 Summer School Particle Physics: Ideas and Recent Development NATO Advanced Institute, Corsica, July 26-August 7, 1999
These are notes from a 15 week course aimed at graduate mathematicians. They provide an essentially self-contained introduction to some of the ideas and terminology of QFT.
The European School of High-Energy Physics is intended to give young physicists an introduction to the theoretical aspects of recent advances in elementary particle physics. These proceedings contain lecture notes on quantum field theory,…
Prepared for the Quantum Field Theory section of the Encyclopedia of Mathematical Physics, Elsevier, 2006. A brief introduction to the methodology and techniques of perturbative relativistic quantum field theory is presented.
These are lecture notes for a mini-course given at the Cornell Probability Summer School in July 2013. Topics include lozenge tilings of polygons and their representation theoretic interpretation, the (q,t)-deformation of those leading to…
This text is the extended version of a talk given at 6th Meeting of Integrable Systems and Quantum Filed Theory at Peyresq hold from June 10 2006 to June 17, 2006 at Peyresq, France. The goal of this lecture is to give a brief introduction…
Lecture notes prepared for the EMS--IAMP Spring School ``Symmetries and Measurement in Quantum Field Theory''. This set of lecture notes covers four lectures: 1. Operator Algebras and Quantum Field Theory, 2. Tomita-Takesaki Modular Theory…
This is a series of lectures intended to introduce high energy theorists to the marvels of the Standard Model from an experimentalist's point of view.
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.