Thank you for your reply. But I am still not sure I understand. A right handed Weyl spinor, will have it's spin pointing along its direction of motion (say x) during its entire existence. Now in the case of an electron, if the spin is along x and I measure it along z, I get half of the time +1/2 and half of the time -1/2. But in the case of the Weyl spinor, I am not even sure what I get. Due to the fact that it is a spin half particle (I think they even used it to describe neutrino) I would expect to also get 50-50 up and down along z. But having right polarization all the time it's spin can't be along the z axis, as it has to be all the time along the x axis. I am just so confused.vanhees71 said:For a Weyl spinor each spin component can take two values ##\pm 1/2##, but the helicity can only be either +1/2 for the right-handed or -1/2 for the left-handed Weyl spinor. The math is nicely summarized at Wikipedia:
https://en.wikipedia.org/wiki/Weyl_equation
The components of a right-handed Weyl spinor are the right-handed particle and the left-handed anti-particle.kelly0303 said:A right handed Weyl spinor, will have it's spin pointing along its direction of motion (say x) during its entire existence.
So for example ##(1,0)^T## can represent a left-handed neutrino and ##(0,1)^T## a right-handed anti-neutrino. Is this right? But can we tell anything about its spin along a given axis, other than the one along it moves? As I said before, if you measure its spin on a direction perpendicular to the direction of motion, what would you get?Orodruin said:The components of a right-handed Weyl spinor are the right-handed particle and the left-handed anti-particle.
In the case of massless neutrinos, they would be left-handed Weyl spinors containing the left-handed neutrino and the right-handed anti-neutrino. We currently have no experimental evidence for the existence of right-handed neutrinos (or left-handed anti-neutrinos).
Weyl spinors are a type of mathematical object used in theoretical physics, specifically in the study of quantum mechanics and particle physics. They were first introduced by physicist Hermann Weyl in the 1920s. Weyl spinors are mathematical representations of fundamental particles, such as electrons, that have spin 1/2.
Helicity is a measure of the spin of a particle along its direction of motion. In Weyl spinors, helicity is closely related to chirality, which is the property of being either left- or right-handed. The helicity of a particle can have important implications for its behavior and interactions with other particles.
Weyl spinors are used to describe the behavior and properties of fundamental particles, such as electrons, in quantum field theory. They are also essential in the study of the Standard Model of particle physics, which describes the interactions of all known particles and their associated forces.
While both Weyl and Dirac spinors are used to describe particles with spin 1/2, they have different mathematical properties. Weyl spinors are two-component objects that only describe particles with a specific chirality, while Dirac spinors are four-component objects that can describe particles with both chiralities. In other words, Weyl spinors are simpler mathematical objects that are used to describe a subset of particles, while Dirac spinors are more complex and can describe a wider range of particles.
Supersymmetry is a theoretical framework that proposes a symmetry between particles with integer spin (bosons) and particles with half-integer spin (fermions). Weyl spinors play a crucial role in this symmetry, as they are used to describe the fermionic particles in supersymmetric theories. In fact, the concept of supersymmetry was first introduced by applying Weyl spinors to the Standard Model of particle physics.