International Journal of Modern Physics A

In this paper we study a class of theories of free particles on the complex plane satisfying a non-Abelian statistics. This kind of particles are generalizations of the anyons and are sometimes called plectons. The peculiarity of these theories is that they are associated to free conformal field theories defined on Riemann surfaces with a discrete and non-Abelian group of authomorphisms D_m. More explicitly, the plectons appear here as “induced vertex operators” that simulate, on the complex plane, the nontrivial topology of the Riemann surface. In order to express the local exchange algebra of the particles, one is led to introduce an R matrix satisfying a multiparameter generalization of the usual Yang-Baxter equations. It is interesting that analogous generalizations have already been investigated in connection with integrable models, in which the spectral parameter takes its values on a Riemann surface that is in many respects similar to the Riemann surfaces we are studying here. The explicit form of the R matrices mentioned above can be also used to define a multiparameter version of the quantum complex hyperplane.

The magnetic moments of the octet baryons are calculated in a chiral symmetric inde-pendent quark potential model of the form

The Hamiltonian canonical formalism of two-dimensional WZNW model based on an arbitrary affine Lie algebra is given under the Chevalley basis. The Poisson brackets of conserved chiral currents are calculated, which turn out to be the classical two-loop Kac-Moody current algebras.

The spinor strong interaction model recently proposed to account for the meson spectra is extended to include interaction with external gauge fields. An action integral is constructed and a restricted variational principle is employed to reproduce the earlier basic meson equations.

In establishing U(1) gauge invariance, the so-called U(1) problem, the absence of pseudoscalar singlet mesons that do not decay strongly, is naturally resolved. SU(2)× U(1) or SO(3) gauge invariance leads to that pseudoscalar isodoublet or isotriplet mesons can generate masses of the gauge bosons without recourse to the unobserved Higgs bosons of the standard electroweak model. The gauge boson masses relate to the linear confinement potential constant of pseudoscalar mesons.

The spinor strong interaction model is quantized in a macroscopic approximation due to the finite size of mesons. Commutation relations and the rest frame Hamiltonian are obtained. In this frame, the relative energy of the quark and antiquark is shown to vanish.

Starting from superdifferential operators in an N=1 superfield formulation, we present a systematic prescription for the derivation of classical N=1 and N=2 super W algebras by imposing a zero-curvature condition on the connection of the corresponding first-order system. We illustrate the procedure on the first nontrivial example (beyond the N=1 superconformal algebra) and also comment on the relation with the Gelfand-Dickey construction of W algebras.

The energy and momentum of the spin model related to the vector representation of the quantized affine algebra of type are computed in the framework of Davies et al. Commutation relations among creation and annihilation operators are also derived.

The affine-Virasoro Ward identities are a system of nonlinear differential equations which describe the correlators of all affine-Virasoro constructions, including rational and irrational conformal field theory. We study the Ward identities in some detail, with several central results. First, we solve for the correlators of the affine-Sugawara nests, which are associated with the nested subgroups g⊃h₁⊃…⊃h_n. We also find an equivalent algebraic formulation which allows us to obtain global solutions across the set of all affine-Virasoro constructions. A particular global solution is discussed which gives the correct nest correlators, exhibits braiding for all affine-Virasoro correlators, and shows good physical behavior, at least for four-point correlators at high level on simple g. In rational and irrational conformal field theory, the high-level fusion rules of the broken affine modules follow the Clebsch-Gordan coefficients of the representations.

We show that it is possible to obtain self-consistent and physically acceptable relativistic classical equations of motion for a pointlike spin-half particle possessing an electric charge and a magnetic dipole moment, directly from a manifestly covariant Lagrangian, if the classical degrees of freedom are appropriately chosen. It is shown that the equations obtained encompass the well-tested Lorentz force and Thomas-Bargmann-Michel-Telegdi spin equations, as well as providing a definite specification of the classical magnetic dipole force, whose exact form has been the subject of recent debate. Radiation reaction — the force and torque on an accelerated particle due to its self-interaction — is neglected at this stage.