Massive twistor particle with spin generated by Souriau–Wess–Zumino term and its quantization

We present a new model of <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mn>4</mn></math> relativistic massive particle with spin and we describe its quantization. The model is obtained by an extension of standard relativistic phase space description of massive spinless particle by adding a new topological Souriau–Wess–Zumino term which depends on spin fourvector variable. We describe equivalently our model as given by the free two-twistor action with suitable constraints. An important tool in our derivation is the spin-dependent twistor shift, which modifies standard Penrose incidence relations. The quantization of the model provides the wave function with correct mass and spin eigenvalues