From the non-trivial nature of the QCD vacuum, the Lagrangian is augmented with a term like

\begin{equation} \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu} \end{equation}

where $ \tilde{G}^{a,\mu \nu} = \frac{1}{2} \epsilon^{\mu \nu \rho \sigma} G^a_{ \rho \sigma} $ is the dual field strength tensor. This term is said to violate CP, giving rise to the strong CP problem.

I understand the CP violation comes from the epsilon tensor in the dual field strength but I am looking for a simple straightforward demonstration of the CP violating nature of a term like $G \tilde{G}$.

  • 2
    $\begingroup$ I have answered this question here: physics.stackexchange.com/a/111178/6178 $\endgroup$ Commented May 26, 2014 at 9:08
  • 1
    $\begingroup$ possible duplicate of Yang-Mills CP violation $\endgroup$ Commented May 26, 2014 at 9:27
  • 1
    $\begingroup$ Ok thanks. Is there another way to answer without using electric and magnetic fields, nor differential forms ? $\endgroup$
    – user42865
    Commented May 26, 2014 at 9:30
  • 9
    $\begingroup$ Well the simplest answer then is what you wrote, namely that it's because the Levi-Civita is a pseudo-tensor, so this term changes sign under parity. $\endgroup$ Commented May 26, 2014 at 9:32


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.