Particle, superparticle, superstring and new approach to twistor theory

A new approach to twistor theory is proposed. The approach is based on certain reformulations of the classical massless particle and superparticle in terms of twistors. The first quantization of these systems leads to a full classification of all the free 4D field theories. The extension of one of this systems to the interacting case leads to a reformulation of the standard Dirac-Yang-Mills field equations in terms of gauge potential which fulfills certain curvatureless conditions in a generalized space (Minkowski+twistor). These conditions are a consequence of integrability conditions of an overdetermined system of linear equations whose vector field is composed from the components of the Dirac field and the Yang-Mills field strength. The twistorial reformulation allows us to gauge away all the ordinary space-time variables. By this procedure we obtain a description of the usual free massless field theories in terms of pure twistor space. These systems are invariant under an infinite dimensional algebra, which contains the two dimensional conformal algebera as a subalgebra. We propose this systems as candidates to a generalization of the notion of two-dimensional conformal field theories to four dimensions. Alternatively, we introduce an extension of the pure twistorial point particle to a two dimensional object, i.e. a pure twistorial string. (author)