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all the extra signs and conjugations and inner products floating around to be able to finish this article without introducing extra sign errors myself. My goal is write this article clearly enough to make it completely obvious exactly how Elko inter-relates to this, and where all the minus signs are going.
189:
If I remember correctly, the
Majorana is its own anti-particle, right? (I mean, that's what "real representation of the Lorentz group" means, under the covers, right? ...there are always subtle points, so I don't want to just wade into this). Thus, the current experiments searching for neutrino-less
885:
Thanks. Yes, that change is reasonable. For me, the meta-issue is the so-called "elko spinor". From what I can tell, some authors ignore it. Others seem to rediscover it. And yet others make some dramatic claims regarding it's quantization, as a dark matter candidate. I am not yet comfortable with
838:
Progress report. All of the above references leave a lot to be desired for both clarity and rigor. I have not found any errors in any of the papers, but the poor structure confused the heck out of me; I finally have a clean and clear and crisp derivation of all of the equations and identities. (Edit
746:
I am trying to fix all of this now, but this is challenging, because all of the texts available are problematic in various ways. I think they're all correct, but they use inconsistent notation and either use squonky, questionable proof techniques, or make questionable statements without providing
869:
I have made a slight edit to the main page, to include the requirement of a
Hermitian operator; this immediately tells you that the mass term must be a skew-symmetric (anti-symmetric) matrix. I think the issues you raised above arise because you ignore the condition of a Hermitian operator. (To
822:
thing, which cannot be done unless this article is done correctly, first. I'm somewhat dubious that the Elko thing is even real, and not some algebra error, but given the nasty state of affairs with the various explanations and derivations of
Majorana that can be found, its quite hard to say.
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Anyone who reads this in the next day or two (or next week or two) is invited to help sort out the, uhhh, current mess. I'm trying to get to it, I really am. BTW, this really is all about trying to get to the
729:
870:
manifest the
Hermiticity, it is more convenient to multiply both sides of the Majorana equation by i, which of course doesn't change the equation, but it highlights that you need a Hermitian operator.)
811:
891:
If you are interested, try reading some of the Elko literature. It is annoyingly low-quality and poorly written, which makes all this harder than it should have been. One starting point is this:
190:
double beta decay are actually looking for
Majorana neutrinos, is that right? Or are there also more complicated spinors that are their own anti-particles? If so, what are they? Just curious.
193:
Anyway, article should mention that no known particles are
Majorana, but that perhaps the neutrinos might be, etc. which is why the see-also section is populated with neutrino-related topics.
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proof, or seem to be built on unfounded assumptions. I thought I could whip this article into shape in a day or two, and instead its becoming a real chore. BTW, I am looking at these:
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Eckart Marsch (2011) "The Two-Component
Majorana Equation-Novel Derivations and Known Symmetries" Journal of Modern Physics, 2011, 2, 1109-1114
83:
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Eckart Marsch (2012) "On the
Majorana Equation: Relations between Its Complex Two-Component and Real Four-Component Eigenfunctions",
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history of this talk page will reveal my confusion). I will update the article tomorrow. Meanwhile, one more curious reference:
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de Gouvêa, A.; Kayser, B.; Mohapatra, R.N. Manifest CP violation from
Majorana phases. Phys. Rev. 2003, D67, 053004.
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but I am not convinced that ... well, that its real and not due to bizarre confusion about sign conventions.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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which was recently AfD'ed. In order to revive it, or some semblance of it, I started to write
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then the kinetic term vanishes. So adding and subtracting these two leads to nonsense.
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It's not in natural units though is it? If it were c and h-bar wouldn't need to appear.
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487:{\displaystyle -i{\partial \!\!\!{\big /}}(\psi +\psi _{c})+\eta m(\psi _{c}-\psi )=0}
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This cannot be right. The reason is easy to see: if these are subtracted one gets
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292:{\displaystyle -i{\partial \!\!\!{\big /}}\psi +m\psi _{c}=0\qquad \qquad (1)}
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378:{\displaystyle i{\partial \!\!\!{\big /}}\psi _{c}+m\psi =0\qquad \qquad (2)}
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International Scholarly Research Network, ISRN Mathematical Physics
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Eckart Marsch, (2013) "A New Route to the Majorana Equation",
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Now if "majorana is it's own antiparticle", that implies that
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724:{\displaystyle -i{\partial \!\!\!{\big /}}\psi _{c}+m\psi =0}
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Palash B. Pal (2011) "Dirac, Majorana and Weyl fermions",
751:
Andreas Aste, (2010) "A Direct Road to Majorana Fields",
665:
Update. Well, eqn 2 is just wrong. It should have been
849:
Phew. This took much more effort than I wanted it to.
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923:Explicit CPT operators for 2-spinor variant
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