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http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism

It is written:

[tex] \mathcal{L} \, = \, \mathcal{L}_{\mathrm{field}} + \mathcal{L}_{\mathrm{int}} = - \frac{1}{4 \mu_0} F^{\alpha \beta} F_{\alpha \beta} + A_{\alpha} J^{\alpha} \,.

[/tex]

a personal calculation with this Lagrangian, I get an off by -1 sign error, so I initially came to the conclusion that this should be:

[tex] \mathcal{L} \, = \, \mathcal{L}_{\mathrm{field}} + \mathcal{L}_{\mathrm{int}} = \frac{1}{4 \mu_0} F^{\alpha \beta} F_{\alpha \beta} + A_{\alpha} J^{\alpha} \,.

[/tex]

Searching online I find disagreement as well. Two examples are:

http://www.wooster.edu/physics/lindner/Ph377Spring2003HW/HW2.pdf [Broken]

http://quantummechanics.ucsd.edu/ph130a/130_notes/node453.html

Am I in error, or are there differences in conventions/definitions that can account for this sign variation?

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# Electrodynamics Lagrangian. differences in sign in online references.

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