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I'm currently studying a course of mechanical analytics. we used some terms that I just can't wrap my head around. I was wandering if anyone could explain\refer me to a good place to read about it:

  1. What is the physical meaning of potential vector of an electric field? How was it discovered?

  2. What’s the connection between potential vector and gauge freedom of the Lagrangian? Could it be given more intuitive meaning?

Perhaps someone could tell me if I got it right: degree of freedom is given when inserting a force in new direction. E.g. take a pendulum. If we make the axis which it rotates around, to move up and down, we’re inserting another degree of freedom. Thus, if we look at a free particle, the vector potential activates a force on the particle and therefore inserts a new degree of freedom?

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