Clifford algebras

Dirac algebra

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).

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Introduction to the Dirac Delta Function

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to the Dirac Delta Function

From playlist Differential Equations

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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

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Dirac delta function

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

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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

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What is linear algebra?

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

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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

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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

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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

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Linear Transformations: Onto

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

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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

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Dirac Delta

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

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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

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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)

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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)

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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

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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

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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)

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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

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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

Related pages

Clifford algebra | Bispinor | Gamma matrices | Klein–Gordon equation | Riemannian geometry | Dirac equation | Representation theory of the Lorentz group | Pauli exclusion principle | Spin group | Spinor | Algebra over a field | Imaginary unit | Spacetime algebra | Higher-dimensional gamma matrices | Complexification | Fierz identity | Exterior algebra | Geometric algebra