No abstract

The superspace formulation of the worldvolume action of twistor string models is considered. It is shown that for the Berkovits-Siegel closed twistor string such a formulation is provided by a N=4 twistor-like action of the tensionless superstring. A similar inverse twistor transform of the open twistor string model (Berkovits model) results in a dynamical system containing two copies of the D = 4, N = 4 superspace coordinate functions, one left-moving and one right-moving, that are glued by the boundary conditions.We also discuss possible candidates for a tensionful superstring action leading to the twistor string in the tensionless limit as well as multidimensional counterparts of twistor strings in the framework of both 'standard' superspace and superspace enlarged by tensorial coordinates (tensorial superspaces), which constitute a natural framework for massless higher spin theories.

We consider a relativistic particle model in an enlarged relativistic phase space, M 18 = (Xµ, Pµ, ηα, ηα, σα, σα, e, φ), which is derived from the free two-twistor dynamics. The spin sector variables (ηα, ηα, σα, σα) satisfy two second class constraints and account for the relativistic spin structure, and the pair (e, φ) describes the electric charge sector. After introducing the Liouville one-form on M 18 , derived by a non-linear transformation of the canonical Liouville one-form on the two-twistor space, we analyze the dynamics described by the first and second class constraints. We use a composite orthogonal basis in four-momentum space to obtain the scalars defining the invariant spin projections. The first-quantized theory provides a consistent set of wave equations, determining the mass, spin, invariant spin projection and electric charge of the relativistic particle. The wavefunction provides a generating functional for free, massive higher spin fields.

We extend the Shirafuji model for massless particles with primary spacetime coordinates and composite four-momenta to a model for massive particles with spin and electric charge. The primary variables in the model are the spacetime four-vector, four scalars describing spin and charge degrees of freedom as well as a pair of Weyl spinors. The geometric description proposed in this paper provides an intermediate step between the free purely twistorial model in two-twistor space in which both spacetime and four-momenta vectors are composite, and the standard particle model, where both spacetime and four-momenta vectors are elementary. We quantize the model and find explicitly the first-quantized wavefunctions describing relativistic particles with mass, spin and electric charge. The spacetime coordinates in the model are not commutative; this leads to a wavefunction that depends only on one covariant projection of the spacetime fourvector (covariantized time coordinate) defining plane wave solutions.