Spinning strings of the Neveu-Schwarz-Ramond type in 3, 4, 6, and 10 space-time dimensions

A model of a spinning string with an internal coordinate index is proposed and studied. When the action for this model is taken to be diagonal in this internal coordinate space and quantized in the light-cone gauge it is foun d to be Lorentz covariant in four-dimensional space-time provided that the internal coordinate space is four dimensional. This combination of space-ti me dimension, D, and internal coordinate space dimension, N, is just one of four possible sets, the other three corresponding to D=3, 6, and 10, preci sely the same values for which it is possible to formulate Yang-Mills theor ies with simple supersymmetry. By comparing the number of propagating degre es of freedom at the zero-mass level in the open string bosonic and fermion ic sectors it is found that a supersymmetric interpretation of this model i s possible provided that all physical states in the bosonic sector have eve n G-parity and the ground-state spinor in the fermionic sector have positiv e chirality. A possible interpretation of the connection between the N comp onents of each of the D space-time coordinates is presented on the basis th at the space-time coordinates are scalars in the internal coordinate space. This interpretation would appear to be reasonable given the fact that the field variables in the Lagrangian density do not necessarily have to repres ent physically measurable quantities but can, instead, only represent physi cally measurable quantities when combined in some manner, the simplest of w hich being a linear combination. The Lagrangian density simply produces the equations of motion and the constraint equations for the independent varia bles, only linear combinations of which represent the four dimensions of ph ysical space-time.