  We solve the quaternionic Dirac equation ($\mathbbm H$DE) in the real Hilbert
space, and we ascertain that their free particle solutions set comprises eight
elements in the case of a massive particle, and a four elements solution set in
the case of a massless particle, a richer situation when compared to the four
elements solutions set of the usual complex Dirac equation ($\mathbbm C$DE).
These free particle solutions were unknown in the previous solutions of
anti-hermitian quaternionic quantum mechanics, and constitute an essential
element in order to build a quaternionic quantum field theory ($\mathbbm
H$QFT).
