Lecture

The Dirac equation for a moving particle

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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 covers the Dirac equation for a moving particle, introducing the Dirac gamma matrices and the slash notation. It explores the properties of the gamma matrices, the Pauli-Dirac representation, the four-vector current, and the adjoint spinor. The lecture delves into the solutions for a moving particle, including the negative energy solutions and antiparticles. It discusses the interpretation of negative energy solutions as antiparticles and presents two approaches to define antiparticle wavefunctions. The lecture concludes with the normalization and orthogonality of the particle and antiparticle spinors.

Instructors (3)

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

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

Official source

Ontological neighbourhood

Physics

Quantum mechanics: Symmetry in quantum mechanics

Related concepts (32)

Pauli matrices

In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (σ), they are occasionally denoted by tau (τ) when used in connection with isospin symmetries. These matrices are named after the physicist Wolfgang Pauli. In quantum mechanics, they occur in the Pauli equation which takes into account the interaction of the spin of a particle with an external electromagnetic field.

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.

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.

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.

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.

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