I have a question about this classical invariance problem I'm working on. I'm almost done, and I understand the theory I think, so my question may seem a bit more math-oriented (it's been a few years since crunching equations). I have found that under a gauge transformation for a single particle in an electric (magnetic) field, the equation of motion is not affected. However, in my final step I have been left with these two extra terms in each component, i.e. these two terms are in my x component: [(1/c)*(d/dx)*(dψ/dt)]-[(d/dx)*(dψ/dt)] , which should equal zero? So my result for the electric field x component is: Ex = [-∇ø-(dAx/dt)]+[(1/c)*(d/dx)*(dψ/dt)]-[(d/dx)*(dψ/dt)] Where I think it should just result in: Ex = [-∇ø-(dAx/dt)] Is there something with the partial differential that I am not recognizing? Or I'm thinking the state change has no impact on the motion? Any help would be greatly appreciated.