As far as I know, the most immediate effects of normal-ordering is the elimination of the zero-point energy (and the zero-point background of any conserved charge) and the elimination of tadpoles in perturbation theory.

In SUSY the zero-point background of all charges is zero, and (in the theories I've studied) there are not tadpoles either. So it seems that normal-ordering is essentially effectless. Is this true to all practical purposes, or is there some point where normal-ordering is useful?

  • $\begingroup$ note: I am using tadpole in its generalised sense: "... diagrams with a propagator that connects back to its originating vertex are often also referred as tadpoles." $\endgroup$ Aug 12, 2017 at 14:13
  • $\begingroup$ note 2: perhaps Apparent failure of SUSY nonrenormalization theorem might be related? $\endgroup$ Aug 12, 2017 at 14:16
  • $\begingroup$ Your "Tadpole" definition also excludes the one-loop correction to the $\phi^4$-Theory. Is that intended? $\endgroup$
    – Neuneck
    Aug 18, 2017 at 12:13
  • $\begingroup$ @Neuneck yes. Note that such a diagram is momentum-independent so it can be entirely reabsorbed into the mass counter-term, so it is essentially irrelevant. $\endgroup$ Aug 18, 2017 at 12:15
  • $\begingroup$ Is your definition of tadpole diagrams the same as self-loop diagrams? $\endgroup$
    – Qmechanic
    Nov 10, 2019 at 14:29


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