Majorana Definition and 61 Threads

In books I find that the Majorana mass term for the neutrinos is given by m_L \nu_L^T C^\dagger \nu where C is Dirac Conjugation operator. How does C look like if I write \nu_L as in terms of its two components \left(\begin{array} (\nu_{L1} \\ \nu_{L2} \end{array} \right)? Is C=...

I have a two component Weyl spinor transforming as \psi \rightarrow M \psi where M is an SL(2) matrix which represents a Lorentz transformation. Suppose another spinor \chi also transforms the same way \chi \rightarrow M \chi. I can write a Lorentz invariant term \psi^T (-i\sigma^2) \chi where...

I wasn't quite sure which forum to use for this, as it covers QM, relativity and geometric algebra, but I'm trying QM for a start. The Dirac equation can be expressed surprisingly simply in the Algebra of Physical Space, as has been shown by W Baylis, and I worked the same thing out...

Hi, one labels the Weyl- and Vector-representations of the Poincare group by (0,1/2), (1/2,0), (1/2,1/2) etc., where does the Majorana spinor fit into this? Or can you say it belongs somehow to the real part of the (0,1/2)+(1/2,0) rep, although this sounds pretty unfamiliar. Thanks for...

It is well known that at times we do need explicit representations for the Dirac gamma matrices while doing calculations with fermions. Recently I found two different expressions for Majorana representation for the gamma matrices. In one paper, the form used is: \gamma_{0} = \left(...

[Moderator's note: Quoted-printable stuff NOT corrected. Sometimes I correct small errors, but a) there are several here and b) it is not obvious what the meaning should be. Please submit only 100% 7-bit ASCII plain-text posts. Even if YOU can read something fancier, many readers can't...

The electromagnetic current vanishes identically in the Majorana case: http://users.jyu.fi/~hetahein/tiede/virta.pdf" . In the case someone cannot open the pdf, here is the formula: \overline{\psi}\gamma^{\mu}\psi = \overline{\psi^{C}}\gamma^{\mu}\psi^{C} =...

A question concerning Feynman rules for Dirac vs Majorana neutrinos. Take e.g. the scattering process: electron + positron -> electron neutrino + electron antineutrino. Following the electroweak Feynman rules we can calculate an expression for the unpolarized differential cross section...

can someone please explain this realistic wave equation i'm new with spinors :)

For my diploma thesis I must provide a calculation that reproduces the results given on page 46 of the paper hep-ph/0309342 . For those who do not want to look it up, I briefly explain what it is about: It concerns the two-body scattering processes (1) N + V => L + H, (2) N + L => V + H, (3) N...

People say that if neutrinos are Majorana particles, they are "identical to their anti particle". But anti neutrinos are obviously different from neutrinos. They produce anti-leptons rather than leptons in the scattering process. So the only difference I can image is the helicity, however that...