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Spinors
Intuitive
A spinor is a mathematical object similar to a vector. However, while a vector points in some spatial direction, like, for example, in the direction of the north pole, a spinor points in a direction in an internal space.
A curious property of a spinor is that if you rotate it by 360° it isn't the same but get's a minus sign. Only after a rotation by 720° a spinor is again the same. In contrast a vector is completely unchanged if you rotate it by 360°.
This crazy property can be illustrated as shown, for example, here:
Concrete
A Dirac spinor field $\Psi$ and its conjugate $\overline\Psi$ are equivalent to two left-handed Weyl spinors $\chi$ and $\tilde\chi$ and their right-handed conjugates $\chi^\dagger$ and $\tilde\chi^\dagger$; $\chi$ and $\chi^\dagger$ describe the left-chiral fermion and the right-chiral antifermion (e.g. \ $e^-_L$ and $e^+_R$), while $\tilde\chi$ and $\tilde\chi^\dagger$ describe the left-chiral antifermion and the right-chiral fermion (e.g. $e^+_L$ and $e^-_R$).
- A nice introduction is An introduction to spinors by Andrew M. Steane
- A Child’s Guide to Spinors by William O. Straub
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