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.