Fermions with cubic and quartic spectrum

We study exotic fermions with spectrum $E^2\propto p^{2N}$. Such spectrum emerges in the vicinity of the Fermi point with multiple topological charge $N$, if special symmetry is obeyed. When this symmetry is violated, the multiple Fermi point typically splits into $N$ elementary Fermi points – Dirac points with $N=1$ and spectrum $E^2\propto p^2$.