Gauge condition


by nrjsingh413
Tags: condition, gauge
nrjsingh413
nrjsingh413 is offline
#1
Apr10-13, 01:07 PM
P: 2
what is physical meaning of Lorentz gauge condition in classical electrodynamics??
Phys.Org News Partner Physics news on Phys.org
Physicists design quantum switches which can be activated by single photons
'Dressed' laser aimed at clouds may be key to inducing rain, lightning
Higher-order nonlinear optical processes observed using the SACLA X-ray free-electron laser
Jano L.
Jano L. is offline
#2
Apr10-13, 02:52 PM
P: 1,027
Actually the constraint

$$
\frac{1}{c^2}\frac{\partial\phi}{\partial t} + \nabla \cdot \mathbf A = 0
$$

is due to Lorenz (Lorenz and Lorentz are easily confused):

https://en.wikipedia.org/wiki/Lorenz_gauge_condition

This equation is sometimes used because it leads to simple and symmetric wave equations for the scalar and vector potential, which are then easily solved for known charge and current distribution and initial conditions on the field.

The potentials are auxiliary functions without direct physical meaning. The meaning of the constraint is really just simplification of the relativistic equations so they become nice and simple.
vanhees71
vanhees71 is offline
#3
Apr11-13, 03:22 AM
Sci Advisor
Thanks
P: 2,136
You confuse me a bit with the speed-of-light factor. In relativistically covariant notation, it's
[tex]\partial_{\mu} A^{\mu}=0.[/tex]
Split into temporal and spatial components this reads
[tex]\partial_0 A^0+\vec{\nabla} \cdot \vec{A}=\frac{1}{c} \partial_t \Phi + \vec{\nabla} \cdot \vec{A}.[/tex]
This is, of course, in Heaviside-Lorentz units.

The good thing with this particular gauge, which should indeed be named after the Danish physicists Ludvig Lorenz instead of the Dutch physicist Hendrik Antoon Lorentz, because Lorenz was the first, using this gauge condition.

The physical merit of this particular gauge is clear: It's a Poincare invariant condition, leading to Poincare invariant equations of motion for the four-potential that at the same time separate into the components. This makes it particularly nice for radiation problems.

For other problems like the description of bound states in quantum mechanics other gauges are more convenient. In this case the Coulomb gauge is good.

It always depends on the physical problem you want to solve, what's the most appropriate gauge constraint. Choosing a gauge is an art comparable to the one to find the most convenient set of coordinates to solve a problem.

andrien
andrien is offline
#4
Apr11-13, 05:15 AM
P: 977

Gauge condition


Quote Quote by nrjsingh413 View Post
what is physical meaning of Lorentz gauge condition in classical electrodynamics??
Can you see that maxwell eqn are total 8 in numbers but there are only 6 quantities to determine.


Register to reply

Related Discussions
Lorentz condition for potential and gauge theory Classical Physics 0
Derivation of gauge condition in linearized GR Special & General Relativity 5
How to arrive at Lorentz gauge condition? Classical Physics 7