Equations for massless and massive spin-1/2 particles with varying speed and neutrino in matter

Understand

The modified Dirac equations describing massless and massive spin-1/2 particles violating the Lorentz invariance are considered.

• The equation for massless fermions with varying speed is formulated in the 16-component first-order form.
• The projection matrix, which is the density matrix, extracting solutions to the equation has been obtained.
• Exact solutions to the equation and energy spectrum for a massive neutrino are obtained in the presence of background matter.