Search results
Results from the WOW.Com Content Network
You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.
The Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge. Stemming directly from Maxwell's equations , these describe the complete, relativistically correct, time-varying electromagnetic field for a point charge in ...
If ϕ is a velocity potential, then ϕ + f(t) is also a velocity potential for u, where f(t) is a scalar function of time and can be constant. Velocity potentials are unique up to a constant, or a function solely of the temporal variable. The Laplacian of a velocity potential is equal to the divergence of the corresponding flow.
The ability to vary the gauge potential at different points in space and time (by changing (,)) without changing the physics is called a local invariance. Electromagnetic theory possess the simplest kind of local gauge symmetry called () (see unitary group). A theory that displays local gauge invariance is called a gauge theory.
Quantum electrodynamics is an abelian gauge theory with the symmetry group U(1) and has one gauge field, the electromagnetic four-potential, with the photon being the gauge boson. The Standard Model is a non-abelian gauge theory with the symmetry group U(1) × SU(2) × SU(3) and has a total of twelve gauge bosons: the photon , three weak bosons ...
The Lorenz gauge hence contradicted Maxwell's original derivation of the EM wave equation by introducing a retardation effect to the Coulomb force and bringing it inside the EM wave equation alongside the time varying electric field, which was introduced in Lorenz's paper "On the identity of the vibrations of light with electrical currents".
Position vectors r and r′ used in the calculation. The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: =, = where φ(r, t) is the electric potential and A(r, t) is the magnetic vector potential, for an arbitrary source of charge density ρ(r, t) and current density J(r, t), and is the D'Alembert operator. [2]
For the leptons, the gauge group can be written SU(2) l × U(1) L × U(1) R. The two U(1) factors can be combined into U(1) Y × U(1) l, where l is the lepton number. Gauging of the lepton number is ruled out by experiment, leaving only the possible gauge group SU(2) L × U(1) Y. A similar argument in the quark sector also gives the same result ...