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Meaning of Square of four vector potential

  1. Mar 8, 2013 #1
    The square of the four vector potential.

    [itex](\phi,A)^2=\phi ^2 - A^2[/itex]

    What's the physical meaning of this lorentz invariant?
    Last edited by a moderator: Mar 8, 2013
  2. jcsd
  3. Mar 8, 2013 #2


    Staff: Mentor

    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.
  4. Mar 16, 2013 #3


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    Science Advisor
    Homework Helper

    hi merrypark3! :smile:

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

    so you can make that invariant anything you like! :wink:
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