Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

The Dirac equation and spin

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 interpretation of the two-fold energy degeneracy in the free particle solutions of the Dirac equation, the non-commutativity of orbital angular momentum with the Dirac Hamiltonian, the definition of the 4x4 spin operator, the concept of helicity, and the discrete symmetries of Parity, Time Reversal, and Charge Conjugation in the context of the Dirac equation.

Instructors (3)

Jan Steggemann

Radoslav Marchevski

Lesya Shchutska

Official source

Ontological neighbourhood

Physics

Particle physics: Standard Model

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.

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.

Spin (physics)

Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. Spin should not be understood as in the "rotating internal mass" sense: spin is a quantized wave property. The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum.

C-symmetry

In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-symmetry is an abbreviation of the phrase "charge conjugation symmetry", and is used in discussions of the symmetry of physical laws under charge-conjugation. Other important discrete symmetries are P-symmetry (parity) and T-symmetry (time reversal).

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.

Related lectures (40)

Dirac Equation: Properties and Solutions

Explores the Dirac equation properties, solutions, antiparticles, and spin concepts.

Symmetries in Particle Physics

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

Symmetries: C/P/T symmetries

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

The Dirac Equation

Explores the development and implications of the Dirac equation, including its solutions, the Dirac sea concept, and the discovery of the anti-electron.

Quantum Field Theory: Particle Interactions