Geometric Algebra - Rotors and Quaternions
In this video, we will take note of the even subalgebra of G(3), see that it is isomorphic to the quaternions and, in particular, the set of rotors, themselves in the even subalgebra, correspond to the set of unit quaternions. This brings the entire subject of quaternions under the heading
From playlist Math
Definition of spherical coordinates | Lecture 33 | Vector Calculus for Engineers
We define the relationship between Cartesian coordinates and spherical coordinates; the position vector in spherical coordinates; the volume element in spherical coordinates; the unit vectors; and how to differentiate the spherical coordinate unit vectors. Join me on Coursera: https://www
From playlist Vector Calculus for Engineers
This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for
From playlist Quaternions
We calculate the functional form of some example spherical harmonics, and discuss their angular dependence.
From playlist Quantum Mechanics Uploads
What is a Four-Vector? Is a Spinor a Four-Vector? | Special Relativity
In special relativity, we are dealing a lot with four-vectors, but what exactly is a four-vector? A four-vector is an object with four entries, which get transformed and changed in a very special way after we change our frame of reference. More precisely, a four-vector transforms like a (1
From playlist Special Relativity, General Relativity
Spinor Lorentz Transformations | How to Boost a Spinor
In this video, we will show you how a Dirac spinor transforms under a Lorentz transformation. Contents: 00:00 Our Goal 00:38 Determining S 01:23 Determining T 02:30 Finite Transformation References: [1] Peskin, Schroeder, "An Introduction to Quantum Field Theory". Follow us on Insta
From playlist Quantum Mechanics, Quantum Field Theory
Exact results in SUSY gauge theories - II by Jaume Gomis
Advanced Strings School 2015 TALKS URL: https://www.icts.res.in/program/all/t... PROGRAM URL: http://www.icts.res.in/program/SS2015 ORGANIZERS: Justin David, Chethan Krishnan and Gautam Mandal DATES: Thursday 11 Jun, 2015 - Thursday 18 Jun, 2015 VENUE: Physics Department, Indian Instit
From playlist Advanced Strings School 2015
Spherical Harmonics and Angular Momentum
We make a connection between spherical harmonics and eigenfunctions of angular momentum.
From playlist Quantum Mechanics Uploads
B03 Simple harmonic oscillation
Explaining simple (idealised) harmonic oscillation, through a second-order ordinary differential equation.
From playlist Physics ONE
Strange Math Books That Will Make You Wonder
We take a look at 10 super interesting math books. These books probably contain math you've never seen before or you didn't know existed. They are pretty cool. The Theory of Spinors: https://amzn.to/3ZyBHv3 The Integration of Functions of a Single Variable: https://amzn.to/40DJj08 Origam
From playlist Book Reviews
Sir Michael Atiyah, What is a Spinor ?
Sir Michael Atiyah, University of Edinburgh What is a Spinor?
From playlist Conférence en l'honneur de Jean-Pierre Bourguignon
Lars Andersson - Geometry and analysis in black hole spacetimes (Part 1)
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity. Following a brief i
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Introduction to Spherical Harmonics
Using separation of variables in spherical coordinates, we arrive at spherical harmonics.
From playlist Quantum Mechanics Uploads
Rudolf Zeidler - Scalar and mean curvature comparison via the Dirac operator
I will explain a spinorial approach towards a comparison and rigidity principle involving scalar and mean curvature for certain warped products over intervals. This is motivated by recent scalar curvature comparison questions of Gromov, in particular distance estimates under lower scalar c
From playlist Talks of Mathematics Münster's reseachers
Jean-Pierre Bourguignon: Revisiting the question of dependence of spinor fields and Dirac [...]
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Geometry
Lars Andersson - Geometry and analysis in black hole spacetimes (Part 3)
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity. Following a brief i
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
A description of curved coordinate systems, including cylindrical and spherical coordinates, and their unit vectors.
From playlist Phys 331 Uploads
Lars Andersson - Geometry and analysis in black hole spacetimes (Part 2)
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity. Following a brief i
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale