Spinors | Dirac equation | Fermions | Partial differential equations
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1⁄2 massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It was validated by accounting for the fine structure of the hydrogen spectrum in a completely rigorous way. The equation also implied the existence of a new form of matter, antimatter, previously unsuspected and unobserved and which was experimentally confirmed several years later. It also provided a theoretical justification for the introduction of several component wave functions in Pauli's phenomenological theory of spin. The wave functions in the Dirac theory are vectors of four complex numbers (known as bispinors), two of which resemble the Pauli wavefunction in the non-relativistic limit, in contrast to the Schrödinger equation which described wave functions of only one complex value. Moreover, in the limit of zero mass, the Dirac equation reduces to the Weyl equation. Although Dirac did not at first fully appreciate the importance of his results, the entailed explanation of spin as a consequence of the union of quantum mechanics and relativity—and the eventual discovery of the positron—represents one of the great triumphs of theoretical physics. This accomplishment has been described as fully on a par with the works of Newton, Maxwell, and Einstein before him. In the context of quantum field theory, the Dirac equation is reinterpreted to describe quantum fields corresponding to spin-1⁄2 particles. The Dirac equation appears on the floor of Westminster Abbey on the plaque commemorating Paul Dirac's life, which was unveiled on 13 November 1995. (Wikipedia).
Introduction to the Dirac Delta Function
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From playlist Differential Equations
From the Dirac Lagrangian to the Dirac Equations | Non-Interacting Lagrangian Density
In this video, we continue with the Dirac Lagrangian which describes spin-1/2 particles in #QuantumMechanics and show how to get the Dirac equation using the Euler-Lagrange equations! If you want to read more about the Dirac equation, we can recommend the book „An Introduction to Quantum
From playlist Dirac Equation
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
Dirac Equation | Gamma Matrices
▶ Topics ◀ Gamma Matrices, Dirac Equation, Clifford Algebra, Anti Commutator ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can suppor
From playlist Dirac Equation
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
Quantum Mechanics 12a - Dirac Equation I
When quantum mechanics and relativity are combined to describe the electron the result is the Dirac equation, presented in 1928. This equation predicts electron spin and the existence of anti-matter.
From playlist Quantum Mechanics
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
(ML 7.7.A1) Dirichlet distribution
Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.
From playlist Machine Learning
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
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
Paul Dirac and the religion of mathematical beauty
Speaker: Graham Farmelo Filmed at The Royal Society, London on Fri 04 Mar 2011 1pm - 2pm http://royalsociety.org/events/2011/paul-dirac/
From playlist Popular talks and lectures
Quantum Mechanics 12b - Dirac Equation II
Here we explore solutions to the Dirac equation corresponding to electrons at rest, in uniform motion and within a hydrogen atom. Part 1: https://youtu.be/OCuaBmAzqek
From playlist Quantum Mechanics
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
Ginestra Bianconi (8/28/21): The topological Dirac operator and the dynamics of topological signals
Topological signals associated not only to nodes but also to links and to the higher dimensional simplices of simplicial complexes are attracting increasing interest in signal processing, machine learning and network science. Typically, topological signals of a given dimension are investig
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Quantum Mechanics 12c - Dirac Equation III
Negative-energy solutions seem to invalidate the Dirac equation. Dirac's bold solution led to the prediction of anti-matter. part b: https://youtu.be/tR6UebCvFqE Quantum field theory playlist: https://youtube.com/playlist?list=PLsp_BbZBIk_6_5pi9tHHmoVJzjqpfBkgJ
From playlist Quantum Mechanics
Solving the Dirac Equation | Rest Frame
In this video, we will show you how to solve the Dirac equation. For now, we will focus on the rest frame of the particle. We will show you in a different video how to arrive at general solutions. 00:00 Review of Dirac Equation 00:33 Plane Wave Ansatz 02:06 Rest Frame 02:41 Dirac Rep. 0
From playlist Quantum Mechanics, Quantum Field Theory
Lecture 6 | New Revolutions in Particle Physics: Basic Concepts
(November 9, 2009) Leonard Susskind gives the sixth lecture of a three-quarter sequence of courses that will explore the new revolutions in particle physics. In this lecture he continues on the subject of quantum field theory, including, the diary equation and Higgs Particles. Leonard S
From playlist Lecture Collection | Particle Physics: Basic Concepts