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Since the only difference between pseudo scalar and a scalar term is just a change of sign under a parity inversion, is it possible that both of them be present in the same field and interact?

For example let's say that the vector gauge field is copuling with some other field. And suppose I have a pseudoscalar mass term like $m\varepsilon^{\mu\nu\rho\sigma}\phi_{\mu\nu}\phi_{\rho\sigma}$ and pure scalar mass term $\frac{M}{16} \phi_{\mu\nu}\phi^{\mu\nu} $. In that case is it possible that both of them present in the same time in the field? Or there is any condition that they have to satisfy?

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    $\begingroup$ Sorry, the terms you wrote aren't scalar mass terms or pseudoscalar mass terms. They're some tensor terms, whatever $\phi_{\mu\nu}$ means. Scalar mass terms - and pseudoscalar, it's almost no difference - are $-m^2 \phi^2/2$. Yes, scalars and pseudoscalars may obviously be parts of the same interacting theory. The condition that has to hold for us to meaningfully talk about scalars or pseudoscalars is the parity symmetry of the theory, at least approximately. $\endgroup$
    – Luboš Motl
    Commented Sep 17, 2012 at 8:31
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    $\begingroup$ You should start with spin-1/2 (scalars are trivial), and add a mass term mixing $m\bar{\psi}\psi$ and $m'\bar{\psi}\gamma^5\psi$, this simply gives the different chiralities making up an uncharged fermion different masses. You can also ask about a massive tensor field, as you did, but then it's complicated since it's a composite particle you are talking about, and you should specify symmetry of the tensor. $\endgroup$
    – Ron Maimon
    Commented Sep 17, 2012 at 9:47
  • $\begingroup$ $\phi_{\mu\nu}$ is anti-symmetric. $\endgroup$
    – aries0152
    Commented Sep 17, 2012 at 10:20
  • $\begingroup$ @Luboš that might make the basis of a good answer (and thanks for confirming what I thought was up with the question) $\endgroup$
    – David Z
    Commented Sep 18, 2012 at 0:18

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