Related papers: Undergraduate Lecture Notes in Topological Quantum…
These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…
We propose a quantum field theory description of the X-cube model of fracton topological order. The field theory is not (and cannot be) a topological quantum field theory (TQFT), since unlike the X-cube model, TQFTs are invariant (i.e.…
These are the lecture notes of the master's course "Quantum Computing", taught at Chalmers University of Technology every fall since 2020, with participation of students from RWTH Aachen and Delft University of Technology. The aim of this…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
This is a very gentle introductory course on quantum mechanics aimed at the first years of the undergraduate level. The basic concepts are introduced, with many applications and illustrations. Contains 12 short chapters of equal length,…
Lecture notes for a one-semester master-level course on analytical mechanics and classical field theory, covering: 0 Mathematical Introduction, 1 Lagrangian Mechanics, 2 Application: Motion in Central Fields, 3 Hamiltonian Mechanics, 4…
We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT) and Noncommutative Floer Homology (NCFH). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that…
The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
These lectures are intended to provide the theoretical basis of describing high-energy particle collisions at a level appropriate to graduate students in experimental high energy physics. They are supposed to be familiar with quantum…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
Numerical simulations of quantum field theories on lattices serve as a fundamental tool for studying the non-perturbative regime of the theories, where analytic tools often fall short. Challenges arise when one takes the continuum limit or…
To understand what does Chern-Simons with compact Lie group(does not like Dijkgraaf-Witten model with finite group in 3d) attach to a point, we first give a construction of Topological Quantum Field Theory(TQFT) via Chern-Simons theory in…
This is a set of lecture notes used in a graduate topic class in applied mathematics called ``Quantum Algorithms for Scientific Computation'' at the Department of Mathematics, UC Berkeley during the fall semester of 2021. These lecture…
In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants. Since then the associated topological quantum field theory (TQFT) has…
This is a set of introductory lecture notes on conformal field theory. Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. It begins with a…
These lectures were originally given at TASI and are directed at a level suitable for graduate students in High Energy Physics. They are intended to give an introduction to the theory and phenomenology of quantum chromodynamics (QCD),…
These notes are an introduction to General Relativity as a Quantum Effective Field Theory, following the material given in a short course on the subject at EPFL. The intent is to develop General Relativity starting from a quantum field…
In these lecture notes, an introduction to topological concepts and methods in studies of gauge field theories is presented. The three paradigms of topological objects, the Nielsen-Olesen vortex of the abelian Higgs model, the 't…
This is a collection of lecture notes from three lectures given by Alexei Kitaev at the 2008 Les Houches summer school "Exact methods in low-dimensional physics and quantum computing." They provide a pedagogical introduction to topological…