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

Inverse fields?

  1. Feb 4, 2016 #1
    Possibly very silly question in QFT. Consider the Lagrangian for a scalar field theory.
    A term like


    should be renormalizable on power counting arguments. The mass dimension of g should be

    2 (D-1)

    where D is the number of space-time dimensions.Does this make sense?
  2. jcsd
  3. Feb 5, 2016 #2
    Isn't there a rule where if the mass dimension is greater than 5, the term is non-renormalizable?
    2(D-1)=6, if D=4.
  4. Feb 5, 2016 #3
    As far as I know, a lagrangian term is not perturbatively renormalizable if it involves a coupling with negative mass dimension.
    Like it happens for gravity or the Fermi model of weak interactions, which works as an effective theory with an energy cutoff.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook