|© | Dror Bar-Natan: Classes: 2013-14: AKT:||< >|
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|Videography by Iva Halacheva||troubleshooting|
|#||Week of...||Notes and Links|
|1||Jan 6|| (PDF). |
: Course introduction, knots and Reidemeister moves, knot colourings.
Tricolourability without Diagrams
: The Gauss linking number combinatorially and as an integral.
: The Schroedinger equation and path integrals.
|2||Jan 13||Homework Assignment 1. |
: The Kauffman bracket and the Jones polynomial.
: Self-linking using swaddling.
: Euler-Lagrange problems, Gaussian integration, volumes of spheres.
|3||Jan 20||Homework Assignment 2. |
: The definition of finite-type and some examples.
: The self-linking number and framings.
: Integrating a polynomial times a Gaussian.
|4||Jan 27||Homework Assignment 3. |
: Chord diagrams and weight systems.
: Swaddling maps and framings, general configuration space integrals.
: Some analysis of .
|5||Feb 3||Homework Assignment 4. |
: 4T, the Fundamental Theorem and universal finite type invariants.
: The Fulton-MacPherson Compactification, Part I.
: More on pushforwards, , and .
|6||Feb 10||Homework Assignment 5. |
: The bracket-rise theorem and the invariance principle.
: The Fulton-MacPherson Compactification, Part II.
: Gauge fixing, the beginning of Feynman diagrams.
|R||Feb 17||Reading Week.|
|7||Feb 24||: A review of Lie algebras. |
: Graph cohomology and .
: More on Feynman diagrams, beginning of gauge theory.
|8||Mar 3|| (PDF) |
: Lie algebraic weight systems.
: Graph cohomology and the construction of .
: Gauge invariance, Chern-Simons, holonomies.
Mar 9 is the last day to drop this class.
|9||Mar 10|| (PDF) |
: The weight system.
: The universal property, hidden faces.
: Insolubility of the quintic, naive expectations for CS perturbation theory.
|10||Mar 17|| (PDF) |
: and PBW.
: The anomaly.
: Faddeev-Popov, part I.
|11||Mar 24|| (PDF) |
: is a bi-algebra.
: Understanding and fixing the anomaly.
Friday: class cancelled.
|12||Mar 31||Monday, Wednesday: class cancelled. |
: A Monday class: back to expansions.
|E||Apr 7||: A Friday class on what we mostly didn't have time to do.|
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Quantum mechanics is a tool or theory in physics that is used to describe the state of the world or a system at the subatomic level. The theory depends on states of the system, observables, measurements and evolution evolution of the system. These are used in building a mathematical model to study quantum mechanics.
In classical mechanics, Newton's laws are used to study physical systems whose behaviour are visible to the human eye. These laws do not apply to systems with quantum effect (this is an effect that cannot be described by classical physics) such as quantum entanglement, radioactive decay and wave particle duality. Such systems are called quantum systems (examples are atoms, molecules, particle on a pendulum etc). Schroedinger equation is one of the tools used in describing such systems.
Schroedinger equation is an equation that describes a systems that has significant of quantum effect. It is a partial differential equation whose solution is a wave function . This is used to study the evolution of the system as time goes by.
The action integral is given by , where is called the Lagrangian.