Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Majorana Lagrangian and Majorana/Dirac matrices

Tags:
  1. Aug 11, 2017 #1
    In Lancaster & Burnell book, "QFT for the gifted amateur", chapter 48, it is explained that, with a special set of ##\gamma## matrices, the Majorana ones, the Dirac equation may describe a fermion which is its own antiparticle.

    Then, a Majorana Lagrangian is considered:
    ##\mathcal{L}=\bar{\nu}i\gamma^\mu\partial_{\mu}\nu- ##mass terms
    where ##\nu## is for the Majorana fields. This Lagrangian is developed, using the usual Dirac ##\gamma## matrices and not the Majorana ones, and good looking Dirac equations are obtained.

    My question is: why using the Dirac matrices to develop the Lagrangian instead of the Majorana ones? If I try the calculation with the Majorana ##\gamma## I obtain odd looking equations that don't look right.

    Thank you for any help.
     
  2. jcsd
  3. Aug 11, 2017 #2

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Look at exercise (36.4).
     
  4. Aug 12, 2017 #3
    >
    Thank you. But is there a unitary transformation between the Majorana ##\bar\gamma## matrices and the Dirac ##\gamma## matrices? I don't think so, for example ##U\bar\gamma^0=\gamma^0U => U=0##. Actually the physics is different with the two sets of matrices, with antiparticle in one case and no antiparticle in the other.
     
  5. Aug 12, 2017 #4

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What do you mean by "usual Dirac ##\gamma## matrices"?

    Which "representation" of the (Dirac) gamma matrices? Dirac? Weyl/chiral (as on page 324)?

    See problem 2 of
    http://users.physik.fu-berlin.de/~jizba/FU-petr/FU-ubungen.pdf

    I think that the first ##U## in the problem should have a ##-\sigma^2## at the bottom left.
     
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: Majorana Lagrangian and Majorana/Dirac matrices
  1. Majorana Equation (Replies: 2)

  2. Majorana Fermion (Replies: 7)

  3. Majorana Hamiltonian (Replies: 1)

Loading...