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The definition of a Majorananeutrino field
For definitness I first discuss the quantitative definition
of a ``Majorana neutrino field''. In this I follow the standard
literature.
Let be a 4component Dirac neurino field^{3}Then, using ``eastcoast'' notation (imaginary time)
the 2component Weyl field is defined^{4} as[1]:
(1) 

The
2component Majorana field is defined via the following
relations by which the neutrino is its own antiparticle
[2]:
(2) 

Here C is the charge conjugation matrix, the
hermitian conjugate and T a transpose acting
only on the spinor,
symbolizes charge conjugation and
a conventional ``creation phase factor''[3]
was set to 1
^{5}.
The definition in eq.(2)
after the semicolon defines the field normalization and
it can be easily shown to
be the one that fulfills the usual
fieldanticommutation axioms of quantumfield theory:
(3) 

where is the field which is canonical conjugate to
.
This field normalisation
(with the factor 1/) is generally used
in the literature[3,8,9,10,11]
^{6}.
Clearly the conditions eq.(1) and eq.(2) are
mathematically mutually exclusive; a Weyl particle can never be
its own antiparticle.
Next: The unitary equivalence of
Up: The nonequivalence of Weyl
Previous: Outline of the paper
Rainer Plaga
20010803