1. Limited time only! Sign up for a free 30min personal 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!

Complicated commutator QFT

  1. Apr 8, 2009 #1
    1. The problem statement, all variables and given/known data

    When calculating this commutator,

    [tex] [ \pi(x), \int d^3x' { \frac{1}{2} \pi^2(x') + \frac{1}{2} \phi(x')(-\nabla^2 + m^2) \phi(x') }] [/tex]

    I almost get the right answer, but not sure if this is valid, or if there is an identity

    3. The attempt at a solution

    when I get to this point

    [tex] \int d^3x' \pi(x) \phi(x')( -\nabla^2 \phi(x')) - \phi(x') (-\nabla^2 \phi(x'))\pi(x) [/tex]

    I need to take out [tex] -\nabla^2 \phi(x') [/tex] to form

    [tex] (-\nabla^2 \phi(x')) [\pi(x), \phi(x')] [/tex]

    that way the rest would follow and give me the correct answer which is

    [tex] -i(-\nabla^2 + m^2)\phi(x')) [/tex]
     
    Last edited: Apr 8, 2009
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted