  It is a well known fact that the usual complex structure on the real Clifford
Algebra (CA) of Minkowski spacetime can be obtained by adding an extra
time-like dimension, instead of the usual complexification of the algebra. In
this article we explore the consequences of this approach and reinterpret known
results in this new context.
  We observe that Dirac particles and antiparticles at rest can be interpreted
as eigenstates of the generator of rotations in the plane formed by the two
time-like coordinates and find an effective finite scale for the extra
dimension when no EM fields are present (without postulating compactness). In
the case of non-vanishing EM fields, we find a gauge condition to preserve such
a scale.

High Energy Physics - Theory