Consider a Majorana spinor(adsbygoogle = window.adsbygoogle || []).push({});

$$

\Phi=\left(\begin{array}{c}\phi\\\phi^\dagger\end{array}\right)

$$

and an pseudoscalar current ##\bar\Phi\gamma^5\Phi##. This term is invariant under hermitian conjugation:

$$

\bar\Phi\gamma^5\Phi\to\bar\Phi\gamma^5\Phi

$$

but if I exploit the two component structure

$$

\bar\Phi\gamma^5\Phi=-\phi\phi+\phi^\dagger\phi^\dagger

$$

the invariance under hermitian conjugation seems lost

$$

-\phi\phi+\phi^\dagger\phi^\dagger\to\phi\phi-\phi^\dagger\phi^\dagger

$$

Where is the catch?

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# Pseudoscalar current of Majorana fields

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