Editing Spinor (section)

=== Consequences ===
There are many far-reaching consequences of the Clebsch–Gordan decompositions of the spinor spaces. The most fundamental of these pertain to Dirac's theory of the electron, among whose basic requirements are
* A manner of regarding the product of two spinors ''{{overline|ϕ}}ψ'' as a scalar. In physical terms, a spinor should determine a [[probability amplitude]] for the [[quantum state]].
* A manner of regarding the product ''ψ{{overline|ϕ}}'' as a vector. This is an essential feature of Dirac's theory, which ties the spinor formalism to the geometry of physical space.
* A manner of regarding a spinor as acting upon a vector, by an expression such as ''ψv{{overline|ψ}}''. In physical terms, this represents an [[electric current]] of Maxwell's [[electromagnetic theory]], or more generally a [[probability current]].