- #1

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Thanks.

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- Thread starter snoopies622
- Start date

- #1

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Thanks.

- #2

jtbell

Mentor

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- #3

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A follow-up question, if I may:

What makes

[tex]

( \frac {\phi }{c} , A^x , A^y , A^z )

[/tex]

a four-vector? That is, why is applying a Lorentz transformation to it vaild? Is the electric potential somehow the time-component of the magnetic potential? Is

[tex]

\vec B = \nabla \times \vec A

[/tex]

still valid if

- #4

dx

Homework Helper

Gold Member

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Is

[tex]

\vec B = \nabla \times \vec A

[/tex]

still valid ifAis four dimensional? Is the curl of a four-dimensional vector field even defined?

The analog of that equation is F

- #5

Meir Achuz

Science Advisor

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[tex](\phi,{\vec A})[/tex] is chosen to be a 4-vector in a LT so that the continuity equationThat is very helpful, thank you.

What makes

[tex]

( \frac {\phi }{c} , A^x , A^y , A^z )

[/tex]

a four-vector? That is, why is applying a Lorentz transformation to it valid? Is the electric potential somehow the time-component of the magnetic potential?

[tex]\partial_\mu A^\mu=0[/tex] will hold in any LT so charge conservation will hold in any Loentz system.

They are no longer called the electric and magnetic potential, but just the 4-vector potential.

- #6

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The thing on the right is the four dimensional curl.

OK, good. Thanks.

[tex](\phi,{\vec A})[/tex] is chosen to be a 4-vector in a LT so that the continuity equation [tex]\partial_\mu A^\mu=0[/tex] will hold in any LT so charge conservation will hold in any Loentz system.

I'm sorry - could you re-word this? I'm not sure I get your meaning.

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