Lecture

The Dirac Equation

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In course

PHYS-415: Particle physics I

Presentation of particle properties, their symmetries and interactions. Introduction to quantum electrodynamics and to the Feynman rules. ...

Description

This lecture discusses the historical context leading to the development of the Dirac equation in 1928, which addressed the issues of negative energy solutions and negative particle densities in the Klein-Gordon equation. The Dirac equation, being first-order throughout, fully described the intrinsic spin and magnetic moment of the electron. It introduces Dirac spinors, four-component wave functions, and Dirac gamma matrices. The solutions of the Dirac equation for particles at rest are explored, revealing positive and negative energy solutions. Dirac's explanation for negative energy solutions, the concept of the Dirac sea, and the discovery of the anti-electron by Anderson in 1932 are also covered. The lecture concludes with the Feynman-Stückelberg Interpretation, proposing the existence of antiparticles for each known particle.

Instructors (3)

Lesya Shchutska

Current Work Our research is focused on testing the boundaries of the Standard Model of particle physics and on looking for new phenomena which might explain unanswered puzzles in the fundamental description of the Universe. The examples of such puzzles would be dark matter nature, matter-antimatter asymmetry of the Universe or very small but non-zero neutrino masses.The main instrument for these tasks is the LHCb detector at CERN, where the analyses of the data collected in the LHC proton-proton collisions

Jan Steggemann

Radoslav Marchevski

Teaching & PhD PhD Students Jou An Chen, Tobias Alexandre Monnard, Xiafei Chang, Gauri Napoletano, Kerim Guseinov, Noémie Duc Courses Particle physics I PHYS-415 Presentation of particle properties, their symmetries and interactions.Introduction to quantum electrodynamics and to the Feynman rules. Particle physics: the flavour frontiers PHYS-471 This course will present experimental aspects of flavour physics primarily in the quark sector but also in the lepton sector and

Official source

Ontological neighbourhood

Physics

Quantum mechanics: Symmetry in quantum mechanics

Related concepts (32)

Dirac equation

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- 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.

Dirac spinor

In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of neutrinos. It appears in the plane-wave solution to the Dirac equation, and is a certain combination of two Weyl spinors, specifically, a bispinor that transforms "spinorially" under the action of the Lorentz group. Dirac spinors are important and interesting in numerous ways. Foremost, they are important as they do describe all of the known fundamental particle fermions in nature; this includes the electron and the quarks.

Dirac sea

The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac equation for relativistic electrons (electrons traveling near the speed of light). The positron, the antimatter counterpart of the electron, was originally conceived of as a hole in the Dirac sea, before its experimental discovery in 1932.

Paul Dirac

Paul Adrien Maurice Dirac (dɪˈræk; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is considered to be one of the founders of quantum mechanics and quantum electrodynamics. He was the Lucasian Professor of Mathematics at the University of Cambridge, a professor of physics at Florida State University and the University of Miami, and a 1933 Nobel Prize in Physics recipient. Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics.

Gamma 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 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.

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