A formulation of relativistic quantum mechanics in twistor space is studied. The phase-space description of the classical theory leads (via canonical quantization) to all known wave equations describing massless particles. A natural link between the classical and the quantum description is provided by the Wigner function de®ned on the space of twistors.

We develop relativistic wave equations in the framework of the new non-hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT -symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no cou...