illuminates
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I have a very simple question. Let's consider the theta term of Lagrangian:
$$L = \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$$
Investigate parity of this term:
$$P(G_{\mu \nu}^a)=+G_{\mu \nu}^a$$
$$P( \tilde{G}^{a, \mu \nu} ) =-G_{\mu \nu}^a$$
It is obvious. But what about ##\theta##? If ##\theta## is simple number then
$$P(\theta)=\theta$$
And in such case we have:
$$P(L)=-L$$
So Lagrangian is P-odd quantity. Is it normal? Is in physics P-odd Lagrangians somewhere else? What about week interaction? Is week interaction conserve parity of Lagrangian?
$$L = \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$$
Investigate parity of this term:
$$P(G_{\mu \nu}^a)=+G_{\mu \nu}^a$$
$$P( \tilde{G}^{a, \mu \nu} ) =-G_{\mu \nu}^a$$
It is obvious. But what about ##\theta##? If ##\theta## is simple number then
$$P(\theta)=\theta$$
And in such case we have:
$$P(L)=-L$$
So Lagrangian is P-odd quantity. Is it normal? Is in physics P-odd Lagrangians somewhere else? What about week interaction? Is week interaction conserve parity of Lagrangian?