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!

Help: Gordon decompositon of the current

  1. May 14, 2012 #1
    Hello:

    A spinless electron can interact with [itex]A^\mu[/itex] only via its charge; the coupling is proportional to [itex](p_{f} + p_{i})^{\mu}[/itex]. An electron with spin, on the other hand, can also interact with the magnetic field via its magnetic moment. This coupling involves the factor [itex]i\sigma^{\mu\nu}(p_{f} - p_{i})[/itex]The relation between the Dirac current and the Klein-Gordon current can be studied as
    follows: Define the antisymmetric sigma tensor as:

    [tex]i\sigma^{\mu\nu} = \frac{i}{2} (\gamma^{\mu}\gamma^{\nu} - \gamma^{\nu}\gamma^{\mu})[/tex]

    And the Gordon decomposition of the Dirac current can be made:

    [tex]\bar u_{f}\gamma^{\mu}u_{i} = \frac{1}{2m} \bar u_{f} [(p_{f} + p_{i})^{\mu} + i\sigma^{\mu\nu} (p_{f} - p_{i})_{\nu} ] u_{i}[/tex]


    To identify the magnetic moment interaction [itex] (-{\mu} . B)[/itex] it suffices to show that:

    [tex] \int[-\frac{e}{2m} \bar \psi_{f} i\sigma_{\mu\nu} (p_{f} - p_{i})^{\nu}\psi_{i}] A^{\mu} d^{3}x = \int\psi^{f*}_{A}(\frac{e}{2m}{\sigma} . B) \psi^{i}_{A} d^{3}x[/tex]


    Can someone please tell me how I can desmostrate this ecuation?
    Thanks.

    P.S.: Exercise 6.2 of "Quarks and Leptons. An Introductory Course in Modern Particle Physics - F.Halzem,A.Martin"
     
  2. jcsd
  3. May 16, 2012 #2

    Bill_K

    User Avatar
    Science Advisor

    elmerx25, All three of your posts have been asking for solutions to homework problems. You need to take a look at the Forum Rules. In particular where it says, "If you are seeking help with a homework/coursework/textbook related issue please post your problem in the appropriate forum in our Homework & Coursework Questions area."
     
  4. May 12, 2014 #3
    How can I send this post to the homework/coursework/textbook area?
    Thanks.
     
  5. May 12, 2014 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I moved the thread.

    What did you find out so far?
     
  6. May 12, 2014 #5
    Hello:

    I have had a sabbatical year without physics. Now I try to continue with my study.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Help: Gordon decompositon of the current
Loading...