Quaternionic (super) twistors extensions and general superspaces

In a attempt to treat a supergravity as a tensor representation, the four-dimensional [Formula: see text]-extended quaternionic superspaces are constructed from the (diffeomorphyc) graded extension of the ordinary Penrose-twistor formulation, performed in a previous work of the authors [D. J. Cirilo-Lombardo and V. N. Pervushin, Int. J. Geom. Methods Mod. Phys., doi: http://dx.doi.org/10.1142/S0219887816501139.], with [Formula: see text] These quaternionic superspaces have [Formula: see text] even-quaternionic coordinates and [Formula: see text] odd-quaternionic coordinates, where each coordinate is a quaternion composed by four [Formula: see text]-fields (bosons and fermions respectively). The fields content as the dimensionality (even and odd sectors) of these superspaces are given and exemplified by selected physical cases. In this case, the number of fields of the supergravity is determined by the number of components of the tensor representation of the four-dimensional [Formula: see text]-extended quaternionic superspaces. The role of tensorial central charges for any [Formula: see text] even [Formula: see text] is elucidated from this theoretical context.

COVARIANT QUANTIZATION OF MASSLESS SUPERPARTICLE IN 4-DIMENSIONAL SPACE-TIME: TWISTOR APPROACH

With the help of Penrose twistor approach by introducing the auxiliary “Stückelberg” degrees of freedom, the “extended” model of massless superparticle is constructed in 4-dimensional space-time, which is equivalent to the original Brink-Schwarz model. The covariant operator quantization of the obtained system is performed in the cases of N=1 and extended supersymmetries. It is shown that there are three independent schemes of quantization of the system at even N, one of which becomes anomalous at odd N.