In mathematical physics, the Dirac algebra is the Clifford algebra . This was introduced by the mathematical physicist P. A. M. Dirac in 1928 in developing the Dirac equation for spin-½ particles with a matrix representation of the gamma matrices, which represent the generators of the algebra. The gamma matrices are a set of four matrices with entries in , that is, elements of , satisfying where by convention, an identity matrix has been suppressed on the right-hand side. The numbers are the components of the Minkowski metric. For this article we fix the signature to be mostly minus, that is, . The Dirac algebra is then the linear span of the identity, the gamma matrices as well as any linearly independent products of the gamma matrices. This forms a finite-dimensional algebra over the field or , with dimension . (Wikipedia).
Introduction to the Dirac Delta Function
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From playlist Differential Equations
Dirac delta function | Lecture 33 | Differential Equations for Engineers
Definition of the Dirac delta function and its Laplace transform. Join me on Coursera: https://www.coursera.org/learn/differential-equations-engineers Lecture notes at http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf Subscribe to my channel: http://www.youtube.co
From playlist Differential Equations for Engineers
Explanation of the Dirac delta function and its Laplace transform. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org/learn/differential-equations-engineers Vector Ca
From playlist Differential Equations
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
This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.
From playlist Linear algebra: theory and implementation
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
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
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
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
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
Dirac Delta Definition In this video, I define the Dirac Delta functional, and show that it is strictly speaking not a function. Along the way, I show that for infinite dimensions, a vector space is not necessarily isomorphic to its dual space. Enjoy! Check out my dual space playlist: ht
From playlist Dual Spaces
Lisa Glaser: A picture of a spectral triple
Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: A compact manifold can be described through a spectral triple, consisting of a Hilbert space H, an algebra of functions A and a Dirac operator D. But what if we are g
From playlist Noncommutative geometry meets topological recursion 2021
Guo Chuang Thiang: What is a Coarse Index, physically?
Talk in Global Noncommutative Geometry Seminar, May 4, 2022
From playlist Global Noncommutative Geometry Seminar (Europe)
Lisa Glaser: Truncated spectral triples on the computer
Talk by Lisa Glaser in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on February 2, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
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
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
Xiang Tang: Cyclic Cocycles for Proper Lie Group Actions
Talk by Xiang Tang in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on February 23, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Physics Ch 67.1 Advanced E&M: Review Vectors (100 of 113) Is The Dirac Delta Function Useless? But..
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn why the Dirac delta function by itself is useless, but…the Dirac delta function is very useful in determining the value
From playlist PHYSICS 67.1 ADVANCED E&M VECTORS & FIELDS
Richard Kerner - Geometry, Matter and Physics
We show how the fundamental statistical properties of quantum fields combined with the superposition principle lead to continuous symmetries including the $SL(2,\mathbb C)$ group and the internal symmetry groups $SU(2)$ and $SU(3)$. The exact colour symmetry is related to ternary $\mathbb
From playlist Combinatorics and Arithmetic for Physics: special days