Meaning of Square of four vector potential

[merrypark3]

The square of the four vector potential.

$(\phi,A)^2=\phi ^2 - A^2$

What's the physical meaning of this lorentz invariant?

 

[Dale]

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.

 

[tiny-tim]

hi merrypark3!

you can add any constant vector to the potential without changing the physics …

so you can make that invariant anything you like!