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Is it possible to have the Dirac sign convention, (-,+,+,+) and at the same time use the metric


i.e have opposing Dirac and metric tensor conventions?

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I do not think so, because you define the metric as:

$$ \operatorname d s^2 = g_{\mu\nu} \operatorname d x^\mu \operatorname d x^\nu $$

If you start using the (-,+,+,+) convention, then you metric needs to be by definition:

$$ \operatorname d s^2 = \operatorname d x^2 + \operatorname d y^2 + \operatorname d z^2 - \operatorname d t^2 $$

If you start using one convention, you need to be consistent.

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yeah i thought so that is annoying, I am working through a paper and I think they use (+,-,-,-) for the metric tensor then when they define the fermionic Hamiltonian it is (-,+,+,+). – user21119 Mar 12 '13 at 20:06
Could you give the link to the paper, you got me interested... Thanks. – gns-ank Mar 13 '13 at 0:07

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