Chiral Quantization on a Group Manifold

The phase space of a particle on a group manifold can be split in left and right sectors, in close analogy with the chiral sectors in Wess Zumino Witten models. We perform a classical analysis of the sectors, and the geometric quantization in the case of $SU(2)$. The quadratic relation, classically identifying $SU(2)$ as the sphere $S^3$, is replaced quantum mechanically by a similar condition on non-commutative operators ('quantum sphere'). The resulting quantum exchange algebra of the chiral group variables is quartic, not quadratic. The fusion of the sectors leads to a Hilbert space that is subtly different from the one obtained by a more direct (un--split) quantization.Comment: 25p, LaTeX, KUL-TF-93/4

High spin particles with spin-mass coupling

The classical and quantum model of high spin particles is proposed and analyzed in this paper. The covariant quantization leads to the spectrum of the particles with the masses correlated with their spins. The particles (and anti-particles) appear to be orphaned as their potential anti-particle partners are of different mass.Comment: 11 pages, 1 figure, the paper accepted for publication in Advances in Applied Clifford Algebr

Light-cone formulation and spin spectrum of non-critical fermionic string

A free fermionic string quantum model is constructed directly in the light-cone variables in the range of dimensions $1<d<10$. It is shown that after the GSO projection this model is equivalent to the fermionic massive string and to the non-critical Rammond-Neveu-Schwarz string. The spin spectrum of the model is analysed. For $d=4$ the character generating functions is obtained and the particle content of first few levels is numerically calculated.Comment: 13 page

High spin particles with spin-mass coupling II

The classical and quantum model of high spin particles with spin-mass coupling is presented in this paper. The mass spectrum of the model is symmetric with respect to particle-antiparticle exchange. The quantum model contains elementary particles and the cluster states generating infinite degeneracy of the mass spectrum.Comment: 12 pages, 1 figure, the paper accepted for publication in Advances in Applied Clifford Algebr

Anomalus BRST Complexes for Non-Critical Massive Strings

It is shown that the BRST resolution of the spaces of physical states of non-critical (anomalus) massive string models can be consistently defined. The appropriate anomalus complexes are obtained by canonical restrictions of the ghost extended spaces to the kernel of curvature operator and additional Gupta-Bleuler like conditions without any modifications of the matter sector. The cohomologies of the polarized anomalus complex are calculated and analyzed in details.Comment: The errors of the previous version are correcte

Non-Critical Light-Cone String

The free non-critical string quantum model is constructed directly in the light-cone variables in the range of dimensions $1<D<25$. The longitudinal degrees of freedom are described by an abstract Verma module. The central charge of this module is restricted by the requirement of the closure of the nonlinear realization of the Poincare algebra. The spin content of the model is analysed. In particular for D=4 the explicit formulae for the character generating functions of the open and closed massive strings are given and the spin spectrum of first 12 excited levels is calculated. It is shown that for the space-time dimension in the range $1<D<25$ the non-critical light-cone string is equivalent to the critical massive string and to the non-critical Nambu-Goto string.Comment: 20 pages, Late

Light-cone formulation and spin spectra of massive strings

It is shown that all bosonic and fermionic massive string models admit consistent light-cone formulations. This result is used to derive the spin generating functions of these models in four dimensions.Comment: 11 page