  Starting from first principles and general assumptions based on the
energy-momentum relation of the Special Theory of Relativity we present a novel
wave equation for ultrarelativistic matter. This wave equation arises when
particles satisfy the condition, $p>>m$, i.e, when the energy-momentum relation
can be approximated by, $E\simeq p+\frac{m^{2}}{2p}$. Interestingly enough,
such as the Dirac equation, it is found that this wave equation includes spin
in a natural way. Furthermore, the free solutions of this wave equation contain
plane waves that are completely equivalent to those of the theory of neutrino
oscillations. Therefore, the theory reproduces some standard results of the
Dirac theory in the limit $p>>m$, but offers the possibility of an explicit
Lorentz Invariance Violation of order, $\mathcal{O}((mc)^{4}/p^{2})$. As a
result, the theory could be useful to test small departures from Dirac equation
and Lorentz Invariance at very high energies. On the other hand, the wave
equation can also describe particles of spin 1 by a simple substitution of the
spin operators, $\boldsymbol{\sigma}\rightarrow\boldsymbol{\alpha}$. In
addition, it naturally admits a Lagrangian formulation and a Hamiltonian
formalism. We also discuss the associated conservation laws that arise through
the symmetry transformations of the Lagrangian.
