Spinors | Articles containing proofs | Clifford algebras | Matrices
In mathematical physics, the gamma matrices, , also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra Cl1,3. It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate spacetime computations in general, and in particular are fundamental to the Dirac equation for relativistic spin-1/2 particles. In , the four contravariant gamma matrices are is the time-like, Hermitian matrix. The other three are space-like, anti-Hermitian matrices. More compactly, , and , where denotes the Kronecker product and the (for j = 1, 2, 3) denote the Pauli matrices. The gamma matrices have a group structure, the gamma group, that is shared by all matrix representations of the group, in any dimension, for any signature of the metric. For example, the Pauli matrices are a set of "gamma" matrices in dimension 3 with metric of Euclidean signature (3, 0). In 5 spacetime dimensions, the 4 gammas above together with the fifth gamma-matrix to be presented below generate the Clifford algebra. (Wikipedia).
Number Theory 1.2 : The Gamma Function
In this video, I introduce the gamma function and show a few properties of it. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Number Theory
Gamma Matrices in Action #2 | How to do Calculations with Gamma Matrices
In this video, we show you how to use Dirac’s gamma matrices to do calculations in relativistic #QuantumMechanics! If you want to read more about the gamma matrices, we can recommend the book „An Introduction to Quantum Field Theory“ by Michael Peskin and Daniel Schroeder, especially cha
From playlist Dirac Equation
The Gamma Function for Half Integer Values
Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy Reflection Formula: https://www.youtube.com/wa
From playlist Number Theory
From playlist Probability Distributions
Gamma Matrices in Action #1 | How to do Calculations with Gamma Matrices
In this video, we show you how to use Dirac’s gamma matrices to do calculations in relativistic #QuantumMechanics! If you want to read more about the gamma matrices, we can recommend the book „An Introduction to Quantum Field Theory“ by Michael Peskin and Daniel Schroeder, especially cha
From playlist Dirac Equation
Gamma Matrices and the Clifford Algebra
In this video, we show you how to use Dirac’s gamma matrices to do calculations in relativistic #QuantumMechanics! If you want to read more about the gamma matrices, we can recommend the book „An Introduction to Quantum Field Theory“ by Michael Peskin and Daniel Schroeder, especially cha
From playlist Dirac Equation
Linear Algebra for Computer Scientists. 12. Introducing the Matrix
This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
Beta Function - Integral Representation Derivation
Today, we derive the integral representation for the Beta function. We will be using this result in a future video to prove the Euler reflection formula!
From playlist Integrals
Relativity's key concept: Lorentz gamma
Einstein’s theory of special relativity is one of the most counterintuitive ideas in physics, for instance, moving clocks record time differently than stationary ones. Central to all of the equations of relativity is the Lorentz factor, also known as gamma. In this video, Fermilab’s Dr. D
From playlist Relativity
QED Prerequisites: The Dirac Equation
In this lesson we give an introduction to the discovery and logic of the Dirac Equation. We introduce the notion of a 4-component spinor field and Dirac Matrices. We do not start developing a solution for this equation, or for the Klein Gordon equation either. There is much more to say abo
From playlist QED- Prerequisite Topics
Richard Kerner - Unifying Colour SU(3) with Z3-Graded Lorentz-Poincaré Algebra
A generalization of Dirac’s equation is presented, incorporating the three-valued colour variable in a way which makes it intertwine with the Lorentz transformations. We show how the Lorentz-Poincaré group must be extended to accomodate both SU(3) and the Lorentz transformations. Both symm
From playlist Combinatorics and Arithmetic for Physics: 02-03 December 2020
Solving Laplacian Systems of Directed Graphs - John Peebles
Computer Science/Discrete Mathematics Seminar II Topic: Solving Laplacian Systems of Directed Graphs Speaker: John Peebles Affiliation: Member, School of Mathematics Date: March 02, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Right-angled Coxeter groups and affine actions ( Lecture 01) by Francois Gueritaud
DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o
From playlist Surface group representations and Projective Structures (2018)
MIT 8.701 Introduction to Nuclear and Particle Physics, Fall 2020 Instructor: Markus Klute View the complete course: https://ocw.mit.edu/8-701F20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Do91PdN978llIsvjKW0au Discussion on how to treat spin in the calculation
From playlist MIT 8.701 Introduction to Nuclear and Particle Physics, Fall 2020
In this tutorial we take a look at elementary matrices. They start life off as identity matrices to which a single elementary row operation is performed. They form the building blocks of Gauss-Jordan elimination. In a future video we will use the to do LU decomposition of matrices.
From playlist Introducing linear algebra
Anosov representations: the basics and maybe more (Lecture 02) by Olivier Guichard
DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o
From playlist Surface group representations and Projective Structures (2018)