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Hi all!

This question concerns flavour changing oscillations. Let's narrow it down to the neutrino case, where we have additionally the violation of lepton numbers. So electron and muon neutrinos naturally follow the relativistic Dirac equation:

[itex] (p\!\!\!/ + m_e ) \nu_e = 0 [/itex] and [itex] (p\!\!\!/ + m_{\mu} ) \nu_{\mu} = 0 [/itex] with [itex] \nu = (\frac{1-\gamma_5}{2}) u_2 [/itex], where [itex] u_2 [/itex] the standard spin down Dirac spinor for particles.

Now when we consider oscillations, we introduce the mass matrix [itex] H_{mass} = \left( \begin{array}{cc} m_{e e} & m_{e \mu} \\ m_{\mu e} & m_{\mu \mu} \end{array} \right) [/itex] and the flavour states apparently follow this strange form of Schroedinger equation:

[itex] i\frac{\partial}{\partial t} \left( \begin{array}{c} \nu_e \\ \nu_{\mu} \end{array} \right) = H_{mass} \left( \begin{array}{c} \nu_e \\ \nu_{\mu} \end{array} \right) [/itex]

I've seen quoted that due to the same space-time dependence we can use the Schroedinger equation even for Dirac neutrinos. I'm clueless to what is going on here and would appreciate any help.

This question concerns flavour changing oscillations. Let's narrow it down to the neutrino case, where we have additionally the violation of lepton numbers. So electron and muon neutrinos naturally follow the relativistic Dirac equation:

[itex] (p\!\!\!/ + m_e ) \nu_e = 0 [/itex] and [itex] (p\!\!\!/ + m_{\mu} ) \nu_{\mu} = 0 [/itex] with [itex] \nu = (\frac{1-\gamma_5}{2}) u_2 [/itex], where [itex] u_2 [/itex] the standard spin down Dirac spinor for particles.

Now when we consider oscillations, we introduce the mass matrix [itex] H_{mass} = \left( \begin{array}{cc} m_{e e} & m_{e \mu} \\ m_{\mu e} & m_{\mu \mu} \end{array} \right) [/itex] and the flavour states apparently follow this strange form of Schroedinger equation:

[itex] i\frac{\partial}{\partial t} \left( \begin{array}{c} \nu_e \\ \nu_{\mu} \end{array} \right) = H_{mass} \left( \begin{array}{c} \nu_e \\ \nu_{\mu} \end{array} \right) [/itex]

I've seen quoted that due to the same space-time dependence we can use the Schroedinger equation even for Dirac neutrinos. I'm clueless to what is going on here and would appreciate any help.

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