1201.5755 (Matej Pavšič)

Localized Propagating Tachyons in Extended Relativity Theories    [PDF]

Matej Pavšič

We examine the possibility of localized propagating tachyonic fields within a
properly extended relativity. A possible extension is to include superluminal
transformations and reference frames. This leads to complex 4D spacetime, or
real 8D spacetime M_{4,4}. The mass shell constraint in M_{4,4} becomes, after
first quantization, the ultrahyperbolic Klein-Gordon equation. The Cauchy
problem for such equation is not well posed, because it is not possible to
freely specify initial data on a 7D hypersurface of M_{4,4}. We explicitly
demonstrate that it is possible to do it on a space-like 4-surface for
bradyons, and on a time-like 4-surface for tachyons. But then the evolution of
a bradyonic field into the four time-like directions, or the "evolution" of a
tachyonic field into the four space-like directions, is not uniquely
determined. We argue that this is perhaps no so bad, because in quantum field
theory (after second quantization) the classical trajectories of fields are not
determined anyway, and so it does not matter, if they are not completely
determined already in the first quantized theory. A next possible extension of
relativity is to consider 16D Clifford space, C, a space whose elements are
oriented r-volumes, r=0,1,2,3,4 of real 4D spacetime. Then the evolution
parameter can be associated with an extra light-cone coordinate, e.g., with the
sum of the scalar and the psudoscalar coordinate, and initial data can be given
on a light-light hypersurface, in which case the Cauchy problem is well posed.
This procedure brings us to the Stueckelberg theory which contains localized
propagating tachyons in 4D spacetime.

View original: http://arxiv.org/abs/1201.5755