  We ask the question whether neutrino physics with momentum space Majorana
spinors, the eigenvectors of the particle--antiparticle conjugation operator,
C=i\gamma_2 K (with K standing for complex conjugation), is different but
physics with Dirac spinors. First we analyze properties of Majorana spinors in
great detail. We show that four dimensional, (4d), Majorana spinors are
unsuited for the construction of a local quantum field because C invariance
does not allow for a covariant propagation in four spinor dimensions, a conduct
due to \gamma_2\gamma_\mu= -\gamma_\mu * \gamma_2. The way out of this dilemma
is finding one more discrete symmetry that respects C invariance and gives rise
to covariant propagators. We construct such a symmetry in observing that the
parity operator, \gamma_0, ``ladders'' between (4d) rest-frame Majorana
spinors, which takes us to eight dimensional spinor spaces. We build up two
types of (8d) spaces-- one with a symmetric- and an other with an
anti-symmetric off diagonal metric and calculate traces of single beta-- and
neutrinoless double beta (0\nu\beta \beta) decays there. We find physics with
(8d) Majorana spinors in the former space to be equivalent to physics with
Dirac spinors in four dimensions. In the latter space we make the rare
observation that in effect of cancellations triggered by the anti-symmetric off
diagonal (8d) metric, the neutrino mass drops from the single beta decay trace
but reappears in 0\nu \beta\beta, without the neutrino being massless in its
free equation-- a curious and in principle experimentally testable signature
for a non-trivial impact of Majorana framework.
