What is "bispinor"

n. (context physics English) An object that is used to describe quantum fields having half-spin

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

$$\psi=\left(\begin{array}{c}\psi_L\\ \psi_R\end{array}\right)$$
consists of two (two-component) Weyl spinors ψ and ψ which transform, correspondingly, under (½,0) and (0,½) representations of the SO(1, 3) group (the Lorentz group without parity transformations). Under parity transformation the Weyl spinors transform into each other.

The Dirac bispinor is connected with the Weyl bispinor by a unitary transformation to the Dirac basis,

$$\psi\rightarrow{1\over\sqrt2}\left[ \begin{array}{cc}1&1\\-1&1 \end{array} \right]\psi= {1\over\sqrt2}\left(\begin{array}{c}\psi_R+\psi_L\\ \psi_R-\psi_L \end{array}\right) .$$
The Dirac basis is the one most widely used in the literature.