Update April 2007
Even though the issue discussed below seemed "very clear" to me in 2002, it was not.
Prompted by an invitation to contribute to the special number of the journal
"Annales de la Fondation Louis de Broglie" on the occasion of the 100th
anniversary of Majorana's birth, I reconsidered the whole issue and
wrote a completely new paper. It explains why a Lagrangian with both
a Majorana mass term and a standard-model interaction term simply admits
no solutions. Neither one of my earlier papers discussed below got this point.
They only understood that the solution with a Majorana mass term must be different
and correctly identified neutrinos as Dirac fields.
The paper (pdf) finally appeared as:
R.Plaga, Annales de la Fondation Louis de Broglie, 31,273-283(2006).
In the editorial introduction to the special number, the editor (Valeri Dvoeglazov) writes:
"...he claims that there are no Majorana physical neutrinos in the standard model.
We discussed this statement in editorial correspondence extensively. I decided
to publish the paper."
Neutrinos are Weyl particles! (2001)
In about 1994 I tried to explain to a friend the nature of Majorana neutrinos,
and in particular the "well known fact" that for massless neutrinos
Majorana and
Weyl neutrinos are equivalent. At that time I was absolutely
sure I understood
this issue quite well. In spite of this after posing me some questions
she said: "You know what Rainer,
I feel you do not really understand this deeply." I became a bit angry:
"No, *you* are
too dumb to understand." A few days later I came back to her and said:
"I am sorry: you were right, I did not understand it at all."
The matter really bugged me and I discussed it in the next two years
with
a couple of knowledgable specialists. In this exchange I shared the
feelings of my friend.
(This was the instinct of a first-year student who immediately notice
when the professor
doesn't know what he's talking about, even if she doesn't know the
first thing about the subject.)
In 1996 I wrote a manuscript about this issue that came to the conclusion
that neutrinos are Weyl particles, and that this can be shown even
in the massless
case. This paper was wrong. In 2001 after countless further discussions
I submitted
a correction (pdf) that reaches the
same conclusion but only when making stronger assumptions.
I also realised neutrinos can have Majorana masses without being Majorana
fermions.
A short summary of my main conclusions, links to various
papers, disussion with
specialists and an explanation where I erred in the
first manuscript can be found here
.
I failed dismally to convince the community, though the issue seems
(by now) very
clear to me. A close colleagues, who knows that I am no fool, refused
to take a look
at it because the issue is "so well understood". In conclusion the
whole matter seems
to be a prime example for the correctness of Popper's motto of this
site.
Ettore
Majorana 1906 - 1938(?) 
Hermann
Weyl 1885 - 1955