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Inverse fields?

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

    g/φ^2

    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.
     
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