I have an equation that says $$C_1\partial_{\mu}G^{\mu\nu}+C_2\frac{1}{2}\epsilon^{\mu\nu\rho\sigma}\partial_{\mu}G_{\rho\sigma}=0$$ If I want to get rid of the ##\epsilon^{\mu\nu\rho\sigma}## in the second term, I know I must multiply the equation by some other ##\epsilon## with different set of indices, but I could use some help in knowing what those incides must be to avoid repeating dummy indices and at the same time being able to end up with an equation with a new epsilon present in the first term (the one with ##C_1##). My aim from all this process is to convert the first ##G^{\mu\nu}## to ##\star G^{\mu\nu}##, i.e., the Hodge dual of ##G^{\mu\nu}##. Any tip will do it, thanks guys!(adsbygoogle = window.adsbygoogle || []).push({});

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# Troubled with the indices

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