Lagrangian, scalar or pseudo-scalar?

  1. Hi,

    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. dextercioby

    dextercioby 12,328
    Science Advisor
    Homework Helper

    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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