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There's an equation from E&M (I believe the definition of the antisymmetric field tensor) that reads:

[tex]

F_{\mu \nu} = \frac{\partial A_\nu}{\partial x^\mu} - \frac{\partial A_\mu}{\partial x^\nu},

[/tex]

where (of course) [itex]A[/itex] is the 4-vector potential. I have no idea how to parse this equation...what's going on with taking the partial of [itex]A_\nu[/itex] with respect to [itex]x^\mu[/itex]? What's this notationdescribing, or telling me todo? I just don't see it.

Also (and this pertains to relativistic quantum mechanics), what's meant by something like

[tex]

\partial_\mu [\partial_\nu \Psi(x^\mu)],

[/tex]

where (of course) [itex]\Psi(x^\mu)[/itex] is the wave function? I.e., what does it mean to operate on [itex]\partial_\nu[/itex] of something with [itex]\partial_\mu[/itex]? Particularly when that something I'm operating on is a function of [itex]x^\mu[/itex]? (By the way: In case the notation is unfamiliar to you, [itex]\partial^\mu = \partial / \partial x_\mu[/itex].) Does that turnintosomething? Can Icompactifythat? Or do I just have to leave it as [itex]\partial_\mu [\partial_\nu \Psi(x^\mu)][/itex]? Also, would I get an equivalent expression if I interchanged the order of [itex]\partial_\mu[/itex] and [itex]\partial_\nu[/itex]; i.e., if I tried to evaluate [itex]\partial_\nu [\partial_\mu \Psi(x^\mu)][/itex]? Or would I get something quite different?

Does all of this boil down to "we need twodistinctdummy indices, [itex]\mu[/itex] and [itex]\nu[/itex], to indicate that there shouldn't be any summation going on?"

(P.S. - I would like to thank David J. Griffiths for getting me into the habit ofitalicizingwords I want to emphasize.)

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# Could someone please explain this 4-vector/tensor notation?

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