EM field, Noether's Theorem and Conservation Theorems

From: David McAnally (D.McAnally_at_i'm_a_gnu.uq.net.au)
Date: 07/13/04 

Date: 13 Jul 2004 13:36:59 GMT

While investigating consequnces of Noether's Theorem for the Lagrangian
density for the electromagnetic field, I found that for any C^2 function
f of x, y, z, t, the following 4-current density is conserved:

        (D.grad f + \rho f, - D df/dt - H x grad f + J f),

i.e. d(D.grad f + \rho f)/dt + div(- D df/dt - H x grad f + J f) = 0.
I was wondering if there was any name for the quantity for which
D.grad f + \rho f is the density and - D df/dt - H x grad f + J f is the
current density. Of course, when f = 1, then the quantity in question is
the charge.

In a similar vein, for any C^2 function f,

        (B.grad f, - B df/dt + E x grad f)

is also a conserved 4-current density.

David

        trilogy, n., a series of three related literary works,
                five if written by Douglas Adams.

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