@AndrewSteane writes in his textbook that a Pauli spinor is a flagpole - with length, direction, flag orientation - and a sign.

A Dirac spinor is a more complicated object. What is the most intuitive visualization of a Dirac spinor?

Update: Steane proposes two flagpoles.

The 8 parameters of a Dirac spinor are 1 magnitude, 3 flagpole angles, 3 boost parameters (such as vx vy vz), and 1 fraction specifying particle and antiparticle components.

Does it make sense to contract the latter 4 numbers into a second flagpole? How can one relate the two descriptions?

  • $\begingroup$ A flagpole and an antimatter flagpole ? $\endgroup$
    – JEB
    Jun 29 at 1:17
  • $\begingroup$ This would be possible: but how does one relate the two poles to the boost parameters? $\endgroup$
    – KlausK
    Jun 29 at 10:40
  • $\begingroup$ Why not 2 spinning flagpoles with opposite chirality $\endgroup$
    – Craig
    Jul 2 at 21:09
  • $\begingroup$ @Craig Steane proposes this as well. But then, how are matter and antimatter flagpoles related to the boost parameters? $\endgroup$
    – KlausK
    Jul 3 at 5:20
  • $\begingroup$ For what its worth I think it's not a great analogy. Nothing will give you intuition for the various spinors except for working with them. $\endgroup$
    – Craig
    Jul 3 at 7:05

1 Answer 1


Andrew Steane also writes, a Dirac spinor is essentially a pair of two Pauli spinors (see An introduction to spinors, chapter "VI. Dirac spinors and particle physics"):

Such a pair is called a bispinor or Dirac spinor. It can conveniently be written as a $4$-component complex vector, in the form $$\Psi=\begin{pmatrix}\phi_R \\ \chi_L\end{pmatrix} \tag{78}$$ where it is understood that each entry is a $2$-component spinor, $\phi_R$ being right-handed and $\chi_L$ left-handed.

Therefore I would visualize a Dirac spinor by a pair of two flagpoles (each with length, direction, flag orientation, and sign).

  • $\begingroup$ He's talking about Weyl spinors. I don't think a Dirac spinor can be interpreted as two Pauli spinors (as I understand the term). $\endgroup$
    – benrg
    Jun 28 at 23:12
  • $\begingroup$ Thank you for the reference! Steane says that a spinor is a flagpole and a sign. But how can a flagpole be right-handed or left-handed? $\endgroup$
    – KlausK
    Jun 29 at 6:27
  • $\begingroup$ @Thomas Fritsch How does one relate the two poles to the boost parameters and to the spin orientation and also to the particle.antparticle ratio? $\endgroup$
    – KlausK
    Jul 1 at 6:32
  • 2
    $\begingroup$ @KlausK I don't know. Sorry. $\endgroup$ Jul 1 at 6:38

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