Supposing you have a lagrangian consisting of $(1/2,0)\oplus (0,1/2)$ representation.

Writing in terms of Weyl fermions, the following terms are possible:

$$-\frac{m_1}{2} (\psi_R^T \epsilon \psi_R - \psi_R^\dagger \epsilon \psi_R^*)$$ $$-\frac{m_2}{2} (\psi_L^T \epsilon \psi_L - \psi_L^\dagger \epsilon \psi_L^*)$$ $$-m_3(\psi_R^\dagger \psi_L + \psi _L^\dagger \psi_R)$$

where $\epsilon = -i \sigma_y$.

Is there anything preventing all three terms from being present at once? Sure, if you have the Majorana constraint $$\psi_r =-\epsilon \psi_L^*$$ then actually all three terms are equal. But I don't see why one must always have this constraint... that constraint seems to be just a choice that one could investigate if one wishes.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.