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Commutator of 4-momentum and position

  1. Oct 12, 2008 #1
    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
    [$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
    Where the generators are defined as


    $J J^{\mu \nu} = i (x^{\mu} \partial^{\nu} - x^{\nu} \partial^{\mu})$
    Last edited: Oct 12, 2008
  2. jcsd
  3. Oct 12, 2008 #2
    Never mind, I found the appropriate relation, [itex] \partial_{\mu}x^{\nu}=g^{\mu \nu} [/itex]

    But I'm not entirely sure why this is true. If someone could explain that would be great.
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