1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?