The two standard conventions for the Minkowski metric are diag(1,-1,-1,-1) and diag(-1,1,1,1). The physics comes out the same either way, but I'm trying to make a list of the things that change depending on the convention you use.(adsbygoogle = window.adsbygoogle || []).push({});

The Klein Gordon equation is one - with the "mostly plus" (MP) metric it is

[tex] (\partial^2 - m^2)\phi = 0[/tex]

and with the "mostly minus" (MM) metric it is

[tex] (\partial^2 + m^2)\phi = 0[/tex]

Another is the sign regarding which is the "positive frequency" solution to Klein Gordon/Dirac. Another is the sign on the Clifford algebra. For MP the more natural choice is

[tex] \{\gamma^{\mu}, \gamma^{\nu}\} = -2\eta^{\mu\nu}[/tex]

and for MM the more natural choice is

[tex] \{\gamma^{\mu}, \gamma^{\nu}\} = 2\eta^{\mu\nu}[/tex]

(you can actually make either choice for either metric but the Dirac equation only has the nice "square root" of the Klein Gordan equation form with these choices.

Can anyone point out some other things that are affected by the convention?

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# Metric Sign Convention

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