Dirac spinor components represent particles and antiparticles with distinct chiralities and spins
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The retrieved physics literature partially touches upon spinor components and wave representations, but does not fully establish that Dirac spinor components distinctly represent particles and antiparticles with specific chiralities and spins.
The notion introduced by Ohanian that spin is a wave property is implemented, both in Dirac and in Schrödinger quantum mechanics. We find that half-integer spin is the consequence of azimuthal dependence in two of the four spinor components, relativistically and non-relativistically. In both cases the spinor components are free particle wavepackets; the total wavefunction is an eigenstate of the total angular momentum in the direction of net particle motion. In the non-relativistic case we make use of the Lévy-Leblond result that four coupled non-relativistic wave equations, equivalent to the Pauli-Schrödinger equation, represent particles of half-integer spin, with g-factor 2. An example of an exact Gaussian solution of the non-relativistic equations is illustrated.
# Interpretation of Dirac Spinor components in Chiral Representation?
Tags: special-relativity, hilbert-space, quantum-electrodynamics, dirac-equation, spinors
- Score: 21
- Views: 6350
- Answers: 2
- Answered: yes
- Asked by: jak (10561 rep)
- Asked: 2014-11-18
- Edited: 2022-04-13
- Site: physics
## Question
I failed to find any book or pdf that explains clearly how we can interpret the different components of a Dirac spinor in the chiral representation and I'm starting to get somewhat desperate. This is such a basic/fundamental topic that I'm really unsure why I can't find anything that explains this concretely. Any book tip, reading recommendation or explanation would be greatly appreciated!
A Dirac spinor is a composite object of two Weyl spinors
\begin{equation} \Psi = \begin{pmatrix} \chi_L \\ \xi_R \end{pmatrix} ,\end{equation}
where in general $\chi \neq \xi$. A special case called Majorana spinor is $\chi=\xi$. The charge conjugated spinor is
\begin{equation} \Psi^c = \begin{pmatrix}
\xi_L \\ \chi_R
\end{pmatrix} . \end{equation}
I want to understand how $\xi_L, \xi_R, \chi_L$ and $\chi_R $, can be interpreted in terms of how they describe particles/antiparticles of
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