meaning of Square of four vector potential

merrypark3

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?

DaleSpam

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!

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merrypark3	meaning of Square of four vector potential Tweet 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?

DaleSpam 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.

tiny-tim Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor	hi merrypark3! you can add any constant vector to the potential without changing the physics … so you can make that invariant anything you like!