# Is the lagrangian always K.E-PE?

1. Oct 5, 2008

### quantumfireball

Is the lagrangian always K.E-PE?????
I dont think so???
so WHAT REALLY is the physical significance of the lagrangian???
Superficially it appears to be KE-PE,but the lagrangian for a charged particle in a vector potential is 1/2MV.V +qV.A-qW.
where V=velocity
A=vector potential
W=Scalar potential.
If the hamiltonion for the above lagrangian is calculated it turns out to be 1/2MV.V+qW.
So what does the term eV.A represent???
It appears to be the interaction energy.
But why does it dissapaer in the hamiltonion.