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
Introduction to Fiber Bundles part 1: Definitions
We give the definition of a fiber bundle with fiber F, trivializations and transition maps. This is a really basic stuff that we use a lot. Here are the topics this sets up: *Associated Bundles/Principal Bundles *Reductions of Structure Groups *Steenrod's Theorem *Torsor structure on arith
From playlist Fiber bundles
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
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
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
Spinors and the Clutching Construction
What’s the connection between spinors and the clutching construction? Chapters: 00:00 Why should we care? 00:32 Spinors in pop culture 01:34 Graph 03:15 Wall 03:42 Tome 04:18 Sir Roger Penrose 04:53 Hopf fibration 06:23 Paul Dirac 07:12 The belt trick 08:54 Exterior derivative 09:49 Deter
From playlist Summer of Math Exposition Youtube Videos
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
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
The TRUTH about TENSORS, Part 9: Vector Bundles
In this video we define vector bundles in full abstraction, of which tangent bundles are a special case.
From playlist The TRUTH about TENSORS
Spin in quantum mechanics is an incredibly interesting property. However, it can be very difficult to understand what exactly it is. In this video, we dispel some misconceptions about spin as well as answer some of the more frequently asked questions about spin. #physics #quantum
From playlist Quantum Mechanics
What is the "spin" of a particle?
“Spin” is one of the core building blocks of quantum reality, but it is a subtle concept to grasp. Here’s Brian Greene with one way to think about it. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Fac
From playlist Science Unplugged: Quantum Mechanics
Introduction to Fiber Bundles Part 4: Torsor Interlude
Torsors and Principal Homogeneous Spaces. What is the difference?
From playlist Fiber bundles
Index Theory and Flexibility in Positive Scalar Curve Geometry -Bernhard Hanke
Emerging Topics Working Group Topic: Index Theory and Flexibility in Positive Scalar Curve Geometry Speaker: Bernhard Hanke Affilaion: Augsburg University Date: October 18, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
An Introduction to Class-S and Tinkertoys (Lecture 1) by Jacques Distler
Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory
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
A panoramic view of Mathematics Research @ICTS by Varun Thakre and Anish Mallick
ICTS In-house 2019 Organizers: Adhip Agarwala, Ganga Prasath, Rahul Kashyap, Gayathri Raman, Priyanka Maity Date and Time: 23rd April, 2019 Venue: Ramanujan Lecture Hall, ICTS Bangalore inhouse@icts.res.in An exclusive day to exchange ideas and discuss research amongst members of ICTS.
From playlist ICTS In-house 2019
Thomas Backdahl - Symmetry operators, conserved currents and energy momentum tensors
Conserved quantities, for example energy and momentum, play a fundamental role in the analysis of dynamics of particles and fields. For field equations, one manifestation of conserved quantities in a broad sense is the existence of symmetry operators, i.e. linear differential operators whi
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Physics, Torque (1 of 13) An Explanation
Explains what torque is, the definition, how it is described and the metric units. Also presented are two examples of how to calculate the torque produced by a force. Torque is a turning force. It is a measure of how much force acting on an object that causes the object to rotate. The ob
From playlist Mechanics