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

How do you interpret quadratic terms in the gauge field in a Lagrangian?

  1. Feb 9, 2010 #1
    Consider a one dimensional gauge theory where the field has mass. The term,

    [tex]m^{2}A^{\mu}A_{\mu}[/tex]

    is the conventional mass term. What if you find terms in your Unified Field Theory lagrangian of the form

    [tex]M_{\mu\nu}A^{\mu}A^{\nu}[/tex] ?

    In this case [tex]M_{\mu\nu}[/tex] is constant.

    When it is not the case that

    [tex]M_{\mu\nu}[/tex]

    is of the form

    [tex]m^{2}g_{\mu\nu}[/tex] ,

    are these to be interpreted as self-interaction terms, or self-interaction terms somehow related to mass for the gauge field, or as bona fide mass terms?
     
  2. jcsd
  3. Feb 9, 2010 #2
    As far as my understanding goes, it's the mass eigenstates that would propagate. This is what we (I, at least) believe happens with neutrinos (with a spinor instead of a vector field, of course). You'd diagonalize your M matrix and find that the mass eigenstates are not identical to flavor eigenstates, but mass eigenstates are ones that diagonalize the Hamiltonian and therefore evolve under an e^(-iHt). Writing down the mass eigenstate at t=0, time-evolving it, then rewriting it in the flavor basis allows you to see the now-popular neutrino oscillations. What IS peculiar, as far as I know, is the fact that the neutrino masses are so small.
     
  4. Feb 9, 2010 #3
    I should also point out that in QED, a mass term like that breaks local gauge invariance and is therefore generally disallowed.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How do you interpret quadratic terms in the gauge field in a Lagrangian?
Loading...