kilokhan
Oct12-08, 12:09 PM
Is there a commutation relation between x^{\mu} and \partial^{\nu} if you treat them as operators? I think I will need that to prove this
[$J J^{\mu \nu}, J^{\rho \sigma}] = i (g^{\nu \rho} J^{\mu \sigma} - g^{\mu
\rho} J^{\nu \sigma} - g^{\nu \sigma} J^{\mu \rho} + g^{\mu \sigma} J^{\nu
\rho})$
Where the generators are defined as
$J J^{\mu \nu} = i (x^{\mu} \partial^{\nu} - x^{\nu} \partial^{\mu})$
[$J J^{\mu \nu}, J^{\rho \sigma}] = i (g^{\nu \rho} J^{\mu \sigma} - g^{\mu
\rho} J^{\nu \sigma} - g^{\nu \sigma} J^{\mu \rho} + g^{\mu \sigma} J^{\nu
\rho})$
Where the generators are defined as
$J J^{\mu \nu} = i (x^{\mu} \partial^{\nu} - x^{\nu} \partial^{\mu})$