I am trying to show that theta-term violates P and CP symmetries,

$$\theta \frac{g^2}{32\pi^2} G^a_{\mu\nu}\tilde{G}^a_{\mu\nu}$$

In the case of QED I could show that this term violates P and CP because theta term can be computed and written in function of electric ($\boldsymbol{E}$) and magnetic field ($\boldsymbol{B}$) and use their definitions from electromagnetic theory as well. However, for non-abelian cases, how could I show that this theta term violates P and CP if I do not have these "physical fields" and I do not know their definitions neither?

  • $\begingroup$ Googling "non-abelian electric field" produces this as a top result. See equations (6) and (7). $\endgroup$ – Richard Myers Apr 12 at 18:15

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