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Lagrangian, scalar or pseudo-scalar?

  1. Jan 10, 2011 #1

    My question is. Can in principle, a Lagrangian density for some theory be a pseudo-scalar. Normally people say that the Lagrangian needs to be a scalar, but it case it is a pseudo-scalar it would also be a eigaen function of the parity operator.

    This topic could well be on the classical physics section, but as this is more relevant in quantum theory I decided to place it here.

  2. jcsd
  3. Jan 10, 2011 #2


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    The normal requirement is that the fields transform irreducibly under the spacetime symmetry group and that the lagrangian density is a scalar under the spacetime symmetry group. The symmetry requirement for QFT in Minkowski spacetime is restricted Poincare group plus CPT plus gauge invariance. The Lagrangian density should be a scalar wrt to the 3 altogether or each taken separately.
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