In theoretical physics, Van der Waerden notation[1][2] refers to the usage of two-component spinors (Weyl spinors) in four spacetime dimensions.
It is named after Bartel Leendert van der Waerden.
Spinors with raised dotted indices, plus an overbar on the symbol (not index), are right-handed, and called anti-chiral indices.
Without the indices, i.e. "index free notation", an overbar is retained on right-handed spinor, since ambiguity arises between chirality when no index is indicated.
For example, if then a spinor in the chiral basis is represented as where In this notation the Dirac adjoint (also called the Dirac conjugate) is