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Also known as Dirac spinor, it was first introduced by Dirac equation proposed by Dirac.

2 Dependence of physical quantities and coordinate directions

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Many physical quantities are not only related to position, but also to the choice of coordinate direction. For example, the quantity of the mark direction vector, whose value is related to the choice of coordinate direction. The transformation property of physical quantity under coordinate rotation transformation can clearly show its dependence on coordinate direction.

The invariant quantity under coordinate transformation is called scalar quantity, and the variable quantity in fixed direction under coordinate transformation is called vector quantity. More components can be coupled by multiple vectors, which have higher order in coordinate transformation and are collectively called tensors. Although the specific values of these quantities may be different when the coordinate directions are different, they always represent a fixed physical quantity. Their numerical changes are only brought about by having to choose coordinates, and they only depend on the choice of coordinates, not the changes of physical quantities themselves.

Scalar, vector and tensor are invariant, and the specific values of components may change with the rotation of coordinates. But they do not contain all quantities with this property. The most basic physical quantity with this property is the spinor. Spinor has four components, and under the coordinate rotation, some specific matrices determine the changes of their respective component values. Our physical space-time is invariant under Lorentz transformation. According to the properties of Lorentz transformation group, spinor is the most basic directional dependence that can be constructed in four-dimensional space-time. The order of dependence of physical quantities on the coordinate direction can be expressed by the corresponding angular momentum, the spinor is 1/2 and the vector is 1. Two spinors can be coupled to a vector, and more spinors can be coupled to a quantity corresponding to 3/2 angular momentum, a tensor corresponding to integer angular momentum, and so on.