# meaning of Square of four vector potential

by merrypark3
Tags: meaning, potential, square, vector
 P: 21 The square of the four vector potential. $(\phi,A)^2=\phi ^2 - A^2$ What's the physical meaning of this lorentz invariant?
 Mentor P: 15,552 If the invariant is timelike then it would be the scalar potential in a frame where the vector position was 0, and if the invariant is spacelike then it would be the magnitude of the vector potential in a frame where the scalar potential is 0. However, unless you are using the Lorentz gauge your gauge condition is frame variant so interpreting it becomes a little strange.
 PF Patron HW Helper Sci Advisor Thanks P: 25,457 hi merrypark3! you can add any constant vector to the potential without changing the physics … so you can make that invariant anything you like!

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