Mathematically, projective twistor space formula_1 is a 3-dimensional complex manifold, complex projective 3-space formula_2. It has the physical interpretation of the space of massless particles with spin. It is the projectivisation of a 4-dimensional complex vector space, non-projective twistor space formula_3 with a Hermitian form of signature (2,2) and a holomorphic volume form. This can be most naturally understood as the space of chiral (Weyl) spinors for the conformal group formula_4 of Minkowski space; it is the fundamental representation of the spin group formula_5 of the conformal group. This definition can be extended to arbitrary dimensions except that beyond dimension four, one defines projective twistor space to be the space of projective pure spinors for the conformal group.