It is a while since I have used these, so can anyone explain to me the meaning of the magnetic vector potential and the electric scalar potential ? I know how to derive them, no problem, but what is their physical meaning?

 

while we are at it... anyone got a good definition for gauge transformations?

Check PAGD.

EAT MY RECURSIVE

Originally posted by Radical Edward

It is a while since I have used these, so can anyone explain to me the meaning of the magnetic vector potential and the electric scalar potential ?

 

The first thing to realize is that they are not physical fields, but mathematical functions from which physical fields are derived.

 

I know how to derive them, no problem, but what is their physical meaning?

 

As I said, they are not physical fields, but they are the elementary fields that appear in the Lagrangian or Hamiltonian. This is because the energy associated with a field is of the form "eV" (charge times scalar potential) and "j.A" (scalar product of current density and vector potential). Since Hamiltonians and Lagrangians deal with energies, you get terms like that.

 

while we are at it... anyone got a good definition for gauge transformations?

 

Yes:

 

For a 4-potential A_u, any transformation of the form:

 

A_u-->A_u'=A_u+:pdif:_uX

 

with :pdif:_u:pdif:^uX=0

 

will leave the physical fields unchanged.

 

Tom

good mathematical definition, thanks, but I don't really get what it means though

The scalar potential should be familiar from Physics II as "energy per unit charge". The vector potential is not so different from that, as it is a kind of "energy per unit current density" (don't take that too literally, as A is still a vector, and energy is not).

 

The Lagrangian and Hamiltonian formulations of dynamics are in terms of energy, and so when dealing with the dynamics of charged particles, terms such as "eV" and "j.A" are thrust upon us.

 

The bit about gauge invariance comes in because the potentials V and A are not uniquely defined for a given E and B.

 

Tom