Bispinor

In physics, a bispinor is an object with four complex components which transform in a specific way under Lorentz transformations: specifically, a bispinor is an element of a 4-dimensional complex vector space considered as a (½,0)⊕(0,½) representation of the Lorentz group. Bispinors are, for example, used to describe relativistic spin-½ wave functions.

In the Weyl basis, a bispinor

consists of two (two-component) Weyl spinors ${\displaystyle \psi _{L}}$ and ${\displaystyle \psi _{R}}$ which transform, correspondingly, under (½,0) and (0,½) representations of the ${\displaystyle SO(1,3)}$ group (the Lorentz group without parity transformations). Under parity transformation the Weyl spinors transform into each other.

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