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In the book Quantum Field Theory by Srednicki, equation 21 for the commutators of the generators of the Lorentz group is

$$[M^{\mu\nu},M^{\rho\sigma}]=i\hbar\Big(g^{\mu\rho}M^{\nu\sigma}-(\mu\leftrightarrow\nu)\Big)-(\rho\leftrightarrow\sigma).$$

Clearly the $\leftrightarrow$ symbol has something to do with the indices, however I'm not sure exactly what it means. Is this notation standard and if so what does it mean?

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It means "repeat the terms I've written, but with these indices swapped". So in your case, $$i\hbar\Big(g^{\mu\rho}M^{\nu\sigma}-(\mu\leftrightarrow\nu)\Big)-(\rho\leftrightarrow\sigma)$$ is short for $$i\hbar\Big(g^{\mu\rho}M^{\nu\sigma}-g^{\nu\rho}M^{\mu\sigma}\Big)-i\hbar\Big(g^{\mu\sigma}M^{\nu\rho}-g^{\nu\sigma}M^{\mu\rho}\Big).$$

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