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

Lecture

Gauge Invariance and Poisson Equation

In course

PHYS-324: Classical electrodynamics

The goal of this course is the study of the physical and conceptual consequences of Maxwell equations. ...

Description

This lecture covers the concept of gauge invariance in solving Maxwell equations, focusing on the Lorenz gauge and its implications. It also discusses the Poisson equation in 3D Euclidean space, providing insights into wave equations and the Laplacian operator.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Victor Gorbenko

Official source

Related concepts (23)

Lorenz gauge condition

In electromagnetism, the Lorenz gauge condition or Lorenz gauge, for Ludvig Lorenz, is a partial gauge fixing of the electromagnetic vector potential by requiring The name is frequently confused with Hendrik Lorentz, who has given his name to many concepts in this field. The condition is Lorentz invariant. The Lorenz gauge condition does not completely determine the gauge: one can still make a gauge transformation where is the four-gradient and is any harmonic scalar function: that is, a scalar function obeying the equation of a massless scalar field).

Gauge theory

In physics, a gauge theory is a field theory in which the Lagrangian is invariant under local transformations according to certain smooth families of operations (Lie groups). The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators.

Gauge fixing

In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space.

Inhomogeneous electromagnetic wave equation

In electromagnetism and applications, an inhomogeneous electromagnetic wave equation, or nonhomogeneous electromagnetic wave equation, is one of a set of wave equations describing the propagation of electromagnetic waves generated by nonzero source charges and currents. The source terms in the wave equations make the partial differential equations inhomogeneous, if the source terms are zero the equations reduce to the homogeneous electromagnetic wave equations. The equations follow from Maxwell's equations.

Maxwell's equations

Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar, etc. They describe how electric and magnetic fields are generated by charges, currents, and changes of the fields.

Related lectures (32)

Cosmological Puzzles: Dark Matter and Energy

Explores fundamental cosmological puzzles related to dark matter and energy.

Gauge Invariance: Electromagnetic Potentials

Explores gauge invariance, electromagnetic potentials, superfluid velocity, and superconductors' magnetic field expulsion.

Electromagnetic Waves

Covers magnetic screening, hysteresis, electromagnetic waves, wave equations, Maxwell's equations, and the electromagnetic spectrum.

Electromagnetic Waves: Basics and Equations

Explores electromagnetic waves, wave equations, solutions, polarization, and energy transport in waves.

Symmetry Breaking: Magnetic Fields in Cosmology