To that end, we here argue in favour of these matrices as physical four-vectors and as such, they must under a Lorentz transformation transform as four-vectors.
3 Dirac [mathematical expression not reproducible]-matrices as a four-vector
If [??] is a vector, then the matrices [[gamma].sup.l] must be components of a 3-vector, so must the matrix [[gamma].sup.0] be the component of the time-vector in the usual four-vector formalism, hence [[gamma].sup.[mu]] must be a four-vector.
4 Dirac equation with the [gamma]-matrices as a four-vector
With [gamma]-matrices now taken as a four-vector, the object [[gamma].sup.[mu]][[partial derivative].sub.[mu]] is a scalar, the meaning of which is that the Dirac equation will now accommodate two types of spinors "the usual Dirac bispinor" and a new "scalar-bispinor", i.e.:
For two tardyonic ("normal") particles of mass [m.sub.e], pair production threshold is reached when the pair is emitted collinearly, with two four-vectors [p.sup.[mu]] = (E, [??]) = ([E.sub.1], [[??].sub.1]) = ([E.sub.2], [[??].sub.2]) that fulfill
Explicit breaking of the Lorentz symmetry may induce faster-than-light dynamics for neutrino wave packets, with a time-like four-vector product [p.sup.[mu]][p.sub.[mu]] > 0 (see [27, 28]).
Upon promotion to a four-vector, one has [[??].sup.[mu]] = (0, [??]).