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Weyl's spinor and Dirac's spinor

What is the difference between the two from a mathematical point of view?
So are there different mathematical definitions of spinor? Is it correct to say that the Weyl spinor appears in the Weyl equation and the Dirac spinor in the Dirac equation? What is the physical meaning of the two equations instead?
The Dirac equation describes the relativistic electron (spin 1/2) while the Weyl equation describes the relativistic fermions (including spin 1/2). What is the difference?

Is it correct to say that a Weyl spinor is an element of the vector space C2 on the field C? (C is the complex field)

Qmechanic
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user332153
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  • One way of understanding the difference involves the representation theory of the Lorentz group. Do you know what a group representation is? Do you know what all the irreducible representations of the Lorentz group are? – G. Smith Dec 07 '20 at 20:15
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    Does this answer your question? Dirac, Weyl and Majorana Spinors – AlmostClueless Dec 07 '20 at 20:17
  • I recommend to have a look https://arxiv.org/abs/1006.1718 - in my opinion, one of the best references, treating the spinors – spiridon_the_sun_rotator Dec 07 '20 at 20:25
  • I would like to know and I understand correctly. Both Weyl and Dirac spinors have spin 1/2 and are therefore representations of fermions.Weyl spinors are "simpler" because they can be right-handed or left-handed (a property called chirality) and remain so under certain transformations. It is therefore said that they are irreducible representations of the Lorentz group. On the contrary, a Dirac spinor is reducible and can be decomposed into a right-handed and a left-handed spinor.A Dirac spinor is therefore said to be the direct product of two Weyl spinors, one right-handed and one left-handed – user332153 Dec 07 '20 at 21:31
  • Weyl spinors are used for those particles whose conjugate complexes (ie the corresponding antiparcels) have the same type of chirality, ie what we have called being "right or left". For example, a left-handed neutrino has an antineutrino counterpart that is always left-handed (curiously for this reason the neutrino is called a vampire particle). The Dirac spinors instead represent particles that have antiparticles of opposite chirality, that is, this property is exchanged in conjugation. Is correct? – user332153 Dec 07 '20 at 21:31

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