Lecture

Dirac Equation: Properties and Solutions

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

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 properties of the Dirac equation, including the introduction of the four Dirac gamma matrices and their properties. It also discusses the solutions of the Dirac equation for free particles at rest and moving particles, as well as the concept of antiparticles. The lecture explores the adjoint spinor, four-vector current, and the concept of helicity for Dirac particles. Additionally, it delves into the charge conjugation, parity, and time reversal operations in the context of the Dirac equation.

Instructors (3)

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

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

Official source

Ontological neighbourhood

Physics

Particle physics: Standard Model

Quantum mechanics: Symmetry in quantum mechanics

Related concepts (32)

C parity

In physics, the C parity or charge parity is a multiplicative quantum number of some particles that describes their behavior under the symmetry operation of charge conjugation. Charge conjugation changes the sign of all quantum charges (that is, additive quantum numbers), including the electrical charge, baryon number and lepton number, and the flavor charges strangeness, charm, bottomness, topness and Isospin (I3). In contrast, it doesn't affect the mass, linear momentum or spin of a particle.

Higher-dimensional gamma matrices

In mathematical physics, higher-dimensional gamma matrices generalize to arbitrary dimension the four-dimensional Gamma matrices of Dirac, which are a mainstay of relativistic quantum mechanics. They are utilized in relativistically invariant wave equations for fermions (such as spinors) in arbitrary space-time dimensions, notably in string theory and supergravity. The Weyl–Brauer matrices provide an explicit construction of higher-dimensional gamma matrices for Weyl spinors.

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.

Four-vector

In special relativity, a four-vector (or 4-vector) is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation of the Lorentz group, the (1/2,1/2) representation. It differs from a Euclidean vector in how its magnitude is determined.

Four-current

In special and general relativity, the four-current (technically the four-current density) is the four-dimensional analogue of the electric current density. Also known as vector current, it is used in the geometric context of four-dimensional spacetime, rather than three-dimensional space and time separately. Mathematically it is a four-vector, and is Lorentz covariant. Analogously, it is possible to have any form of "current density", meaning the flow of a quantity per unit time per unit area.

Related lectures (64)

Symmetries: C/P/T symmetries

Covers the symmetries of empty space, including Parity, Time reversal, and charge conjugation, with examples from Quantum Electrodynamics.

Quantum Field Theory: Particle Interactions

Explores the Dirac equation, Pauli-Dirac representation, particle solutions, operators, particle types, Feynman diagrams, and quantum electrodynamics.

Discrete Symmetries: Asymptotic States and S-matrix

Covers the concept of discrete symmetries, focusing on the introduction to asymptotic states and S-matrix.

Symmetries in Particle Physics

Explores symmetries in particle physics, covering parity, charge conjugation, fermion quantum numbers, chirality, and their applications in understanding particle interactions.

Discrete Symmetries: Introduction