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Starting from first principles and general assumptions based on theenergy-momentum relation of the Special Theory of Relativity we present a novelwave equation for ultrarelativistic matter. This wave equation arises whenparticles satisfy the condition, $p>>m$, i.e, when the energy-momentum relationcan 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 spinin a natural way. Furthermore, the free solutions of this wave equation containplane waves that are completely equivalent to those of the theory of neutrinooscillations. Therefore, the theory reproduces some standard results of theDirac theory in the limit $p>>m$, but offers the possibility of an explicitLorentz Invariance Violation of order, $\mathcal{O}((mc)^{4}/p^{2})$. As aresult, the theory could be useful to test small departures from Dirac equationand Lorentz Invariance at very high energies. On the other hand, the waveequation can also describe particles of spin 1 by a simple substitution of thespin operators, $\boldsymbol{\sigma}\rightarrow\boldsymbol{\alpha}$. Inaddition, it naturally admits a Lagrangian formulation and a Hamiltonianformalism. We also discuss the associated conservation laws that arise throughthe symmetry transformations of the Lagrangian.

New wave equation for ultrarelativistic particles