Majorana Definition and 55 Threads

$$i \gamma^{\mu} \partial_{\mu} \psi = m \psi_c \\ i \gamma^{\mu} \partial_{\mu} \psi_c = m \psi $$ Where ##\psi_c = C \gamma^0 \psi^*## Show that the above equations can be obtained from the followong lagrangian $$ L = \overline{\psi} i \gamma^{\mu} \partial_{\mu} \psi - \frac{1}{2} m \left...

[Moderator's note: Spin-off from previous thread due to topic change.] A Majorana mass term is completely different physics from a neutrino oscillating to an antineutrino.

https://arxiv.org/abs/2207.02472 InAs-Al Hybrid Devices Passing the Topological Gap Protocol "We present measurements and simulations of semiconductor-superconductor heterostructure devices that are consistent with the observation of topological superconductivity and Majorana zero modes."...

In the article by E. Majorana "Oriented atoms in a variable magnetic field", in particular, it's considered (and solved) the problem of describing a state with spin J using 2J points on the Bloch sphere. That is, if the general state of the spin system , (1) then, according...

Hello! I don't know much about this topic so I am sorry if my question is silly. As far as I understand if neutrinos are Majorana particles, one consequence is that neutrinos are their own antiparticles. This can be observed, for example, in neutrinoless double beta decay. However, if we take...

Hello! In the attached plot, we have the Majorana mass as a function of the lightest neutrino for the normal (m1<m2<m3) and inverted (m3<m1<m2) hierarchy. Plugging in the values from the PMNS matrix in the formula for Majorana mass, I get something of the form: ##m_{\beta\beta} =...

If neutrinos are majorana particles does this mean that lepton number is not conserved in particle reactions? And I only noticed neutrinos are only produced when the decay of a particle to some other particles is carried by the W bosons ( weak interaction ). Is it possible the weak interaction...

For a Majorana neutrino in matter we have the equation $$(i\gamma^{\mu}\partial_{\mu}-A\gamma_{0})\nu_{L} = m\overline{\nu_{L}}.$$ A is to be considered constant. Squaring, in the ultra-relativistic limit one obtains the dispersion relation $$(E-A)^{2}-p^{2} \simeq mm^{\dagger}$$ i.e. $$p...

Acoording to the internet, majorana fermions are particles which its antiparticle is itself. But shouldn't particles and antiparticles annihilate each other? Then how could such particle exist or being predicted?

I`ve spent some time reading about the baryon asymmetry and the Sakharov`s conditions, and there some things I didn't exactly get: 1. Interactions out of thermal equilibrium: isn't it trivial? our universe is expanding so, of course, it out of equilibrium. 2. CP violation: I`ve read that Cronin...

Background The Standard Model conserves baryon number, which is equal to (quarks divided by three) minus (anti-quarks divided by three) and lepton number, which is equal to leptons minus antileptons, separately, except in sphaleron processes which conserve B-L, but not B or L separately. There...

In Lancaster & Burnell book, "QFT for the gifted amateur", chapter 48, it is explained that, with a special set of ##\gamma## matrices, the Majorana ones, the Dirac equation may describe a fermion which is its own antiparticle. Then, a Majorana Lagrangian is considered...

http://www.independent.co.uk/news/science/angel-particle-anti-matter-quantum-physics-discover-stanford-university-california-irvine-a7851661.html

\bf{Setup} Hi! I am trying to derive the wavefunctions of the zero energy solutions of the Schrodinger equation in a 1D p-wave superconductor (Kitaev model). I am starting with the Hamiltonian $$ \begin{equation} H = \left[\begin{array}{cc} \epsilon_k & \Delta^{\ast}_k\\ \Delta_k & -\epsilon_k...

So we are not yet sure exactly what mechanism accounts for the neutrino masses. One possible mechanism is the seesaw mechanism. Am I correct in thinking: Majorana mass terms are born from couplings between particles and antiparticles. This violates lepton number conservation and charge...

Hello, I am having a real problem trying to figure out what a Majorana mass is. The only thing I gather so far is that dirac mass is the mass that is the result of the Higgs Mechanism. What exactly is the Majorana mass, and for which particles does it exist.Thank you

Say ##L## and ##L^{c}## are a pair of ##SU(2)## doublets (electroweak-charge fermions) and ##N_{1}## and ##N_{1}^{c}## are a pair of neutral Majorana fermions. Say that these fermions couple to the Higgs via Yukawa coupling and have vector masses ##M_0## and ##M_1## respectively...

I need to know if the Symplectic Majorana spinors in 5 dimension have any advantage with respect to the Dirac spinors in 5 dimension, since they have the same number of components. For example if the Symplectic Majorana spinors have a manifested symmetry that the Dirac spinors don't have, or if...

Consider a Majorana spinor $$ \Phi=\left(\begin{array}{c}\phi\\\phi^\dagger\end{array}\right) $$ and an pseudoscalar current ##\bar\Phi\gamma^5\Phi##. This term is invariant under hermitian conjugation: $$ \bar\Phi\gamma^5\Phi\to\bar\Phi\gamma^5\Phi $$ but if I exploit the two component...

Dirac description If I well understood a Dirac description for fermions is : ##\Psi_{D}=\Psi_{L}+\Psi_{R}## where ##\Psi_{L}## is the left-chiral spinor and ##\Psi_{R}## the right-chiral spinor. Each spinor, ##\Psi_{L} ## and ##\Psi_{R}## has 2 components cotrresponding to the particle and...

My question concerns the chirality vs helicity for massive neutrinos. I know that as the mass is really light we can usually approximate helicity = chirality. But I would like to consider the exact case with the mass : i.e left handed (chirality )neutrino propagates with both left and right...

Hi everyone, I was watching a TV programme the other day, where they talked about an Italian physicist, Ettore Majorana, who disappeared in 1938: http://en.wikipedia.org/wiki/Ettore_Majorana Apparently they've recently found evidence that he lived in Venezuela in the 50's, and that his...

Hello Why are neutrino oscillations insensitive to Majorana phases? I'm guessing it has something to do with them being factored out the PMNS matrix using a diagonal matrix ... i.e. U_PMNS = U Diag (a1, a2, 1) Is there a point in the oscillation calculation where they always cancel due to a...

http://thewestsidestory.net/2014/10/05/18346/obscure-majorna-particle-discovered-encompasses-matter-antimatter/ Reports the direct observation of Majorana particles, by Princeton researchers. Is there anything substantive to this? - or is it just a Science writer getting it wrong?

Hi, I recently attended several lectures on the topic of neutrino astrophysics. I wanted to verify some of the fact that I gleaned for them, specifically about the Dirac vs Majorana nature of neutrinos. 1) The most basic fact first. If a neutrino is Dirac in nature, then it has 3 flavors...

This question is probably very over-simplistic, however: if neutrinos are majorana particles, which are their own antiparticles, how could they still be CP violating? I don't understand precisely how this would work, but physicists I have spoken to said that neutrinos being majorana could...

http://www.eurekalert.org/pub_releases/2013-06/vu-stm061013.php http://arxiv.org/abs/1211.0503 Anapole Dark Matter Chiu Man Ho, Robert J. Scherrer (Submitted on 2 Nov 2012) We consider dark matter (DM) that interacts with ordinary matter exclusively through an electromagnetic anapole, which...

Does anyone have any good technical papers covering the Majorana particle? http://www.newscientist.com/article/mg21829160.300-nothing-to-see-the-man-who-made-a-majorana-particle.html

Let \gamma^{\rho} \in M_{4}(\mathbb{R}) be the Majorana representation of the Dirac algebra (in spacetime signature \eta_{00} = -1), and consider the Majorana Lagrangian \mathcal{L} = \mathrm{i} \theta^{\mathrm{T}} \gamma^{0} (\gamma^{\rho} \partial_{\rho} - m) \theta, where \theta is a...

The Majorana mass term is expressed from a single Weyl spinor. But I am a little confused by the expression. For example, see Eq. (2) in http://arxiv.org/pdf/hep-ph/0410370v2.pdf \mathcal{L}=\frac{1}{2}m(\chi^T\epsilon \chi+h.c.) Here \chi is the Weyl spinor and \epsilon = i\sigma^2 is...

http://science.slashdot.org/story/12/04/13/1547242/scientists-find-long-sought-majorana-particle Is this legitimate? I tried reading the original paper but my physics skills weren't quite enough to keep up with it.

Published in “Science Online” 12 April 2012: “Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices” by V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven Abstract Majorana fermions are particles identical to...

Why do Majorana particles occur? For example, why is the antiparticle of photon itself?

I'm just wondering how the Majorana matrices first were found. I have only seen them immediately written down at different webpages, and never seen a derivation. Is it obvious how to transform the Dirac gamma matrices into the Majorana representation?

Hi everyone, this has been bothering me for a while and even though I've done some light reading on this topic I am struggling to understand it. I know that theory states that we do not see left handed antineutrinos or right handed neutrinos and this is where cp violations comes from. But...

The Dirac propagator (e.g. for an electron) is given by the inverse of the field equation in momentum space i.e. (\displaystyle{\not} p - m)\psi = 0, which gives: \frac{i}{(\displaystyle{\not} p - m)} = \frac{i(\displaystyle{\not} p + m)}{(p^2-m^2)}. So is the propagator for a Majorana...

My interests are in astrophysics, so please forgive my ignorance of particle physics. I've just read Frank Close's book, "Neutrino"---excellent read, I'd recommend it---in which he points out that Ray Davis' first experiments to detect neutrinos from nuclear reactors (with no detections)...

As I understand, the answer will have to come from neutrino-less double beta decay experiments. When will these experiments reach the required sensitivity and gather enough data, to provide us with a definite answer about the nature of neutrinos?

For example, the right-handed sneutrino. It can decay into both (s)leptons and anti-(s)leptons, so it is also the anti-particle of itself. I wonder how it looks like mathematically. If it is the same as normal scalar field, we can still distinguish its anti-particle (the complex conjugate)...

Can anyone explain to me what is the difference between a Weyl spinnor and a Majorana spinnor? Thanks

Hi, So if we have an interaction Lagrangian for a Majorana field: L_1=\tfrac{1}{2} g\phi\Psi^{T}C\Psi Now looking at the path integral, I believe this must go like: Z (\eta^{T},J) ~ \exp{[\tfrac{1}{2} ig \int\,\mathrm{d}^4x (\tfrac{1}{i}\tfrac{\delta}{\delta J(x)...

Amusingly, a search on these three words here in PF does not show a lot of postings, so I am creating this thread so you can ask all your doubts about N-dimensional Majorana, Weyl and Dirac particles, their representations, their Lagragians, masses, and whatever you have always wanted to know...

Hi, By analogy with scalar field case, Srednicki leads us to Z_0 (\eta)=\int \mathcal{D}\Psi \exp{\left[i\int\,\mathrm{d}^4x (\mathcal{L}_0+\eta^{T}\psi)\right]} for a Majorana field. I was expecting something different, like maybe: Z_0 (\eta)=\int...

Hi... Recently read that neutrinos can be Majorana particles only because they are singlets under the unbroken U(1) electromagnetic.. I can understand that...Majorana means that the particle is its own antiparticle..this can't happen if it is charged, as the antiparticle should have...

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...