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fzero
#2
Jul18-11, 02:41 PM
Sci Advisor
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PF Gold
P: 2,602
Symmetry of the metric ([itex]g^{\mu \nu}=g^{\nu \mu}[/itex]) and total antisymmetry of [itex] \epsilon_{\alpha \mu \beta \nu}[/itex] imply that [itex]\epsilon_{\alpha \mu \beta \nu}g^{\mu \nu}=0[/itex] (together with all possible permutations of indices). So all terms of that form vanish.