kilokhan
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Is there a commutation relation between [itex]x^{\mu}[/itex] and [itex]\partial^{\nu}[/itex] if you treat them as operators? I think I will need that to prove this
[itex] [$J J^{\mu \nu}, J^{\rho \sigma}] = i (g^{\nu \rho} J^{\mu \sigma} - g^{\mu<br /> \rho} J^{\nu \sigma} - g^{\nu \sigma} J^{\mu \rho} + g^{\mu \sigma} J^{\nu<br /> \rho})$[/itex]
Where the generators are defined as
[itex] <br /> $J J^{\mu \nu} = i (x^{\mu} \partial^{\nu} - x^{\nu} \partial^{\mu})$[/itex]
[itex] [$J J^{\mu \nu}, J^{\rho \sigma}] = i (g^{\nu \rho} J^{\mu \sigma} - g^{\mu<br /> \rho} J^{\nu \sigma} - g^{\nu \sigma} J^{\mu \rho} + g^{\mu \sigma} J^{\nu<br /> \rho})$[/itex]
Where the generators are defined as
[itex] <br /> $J J^{\mu \nu} = i (x^{\mu} \partial^{\nu} - x^{\nu} \partial^{\mu})$[/itex]
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