WIGNER THEORY OF THE NAMBU STRING: (I) THE OPEN STRING

Abstract

A set of relative variables for the open string with P2>0 is found, which has Wigner covariance properties. It allows one to obtain global Lorentz-invariant abelianizations of the constraints, and then to find global Lorentz-invariant canonically conjugated gauge variables. By means of the multitemporal approach a noncanonical redundant set of Dirac observables is defined; these transform as spin-1 Wigner vectors and satisfy constraints of the type of σ models. The generalized Virasoro algebra, except for L0, lives entirely in the gauge sector of the theory. The original canonical variables are expressed by means of the resulting generalized harmonic analysis in terms of these observables, and of the noncovariant center-of-mass ones. Quantization is not done, because a canonical basis of observables is still lacking, but the program to find them is expounded: instead of making a reduction from O (D–1)(P) to O (D–2), which would give a nonlinear realization of the Poincaré group like in the noncovariant approach, one has to find a Thomas-spin-adapted basis of observables which are Lorentz-invariant (except for three of them).