Let's say that some non-operator (having only numbers as it's components) tensor is antisymmetric:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\omega^{\sigma\nu}=-\omega^{\nu\sigma}[/tex]

and

[tex]\omega_{\sigma\nu}=-\omega_{\nu\sigma}[/tex],

however, I have read in the Srednicki book that it is incorrect to say that the same tensor with one index down and one up would be antisymmetric as well.

Could you please point out, where and what are the errors of the derivation? Should I read something before asking such questions? g here is the Minkowski metric:

[tex]\omega^{\nu}\,_{\sigma}=\omega^{\nu\beta}g_{\beta\sigma}=-\omega^{\beta\nu}g_{\beta\sigma}=-\omega_{\sigma}\,^{\nu}

[/tex]

Thank you.

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# Anitsymmetric tensor/switching indices problem

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