International Journal of Modern Physics A

The problem of the proper inclusion of spin in Aharonov—Bohm scattering is considered. It is proposed that this should be accomplished by imposing the requirement that all singularities arising from the presence of spin in the associated wave equations be interpreted as limits of physically realizable flux distributions. This leads to results which confirm the usual cross section in the spinless case but imply nontrivial modifications for the scattering of a polarized spin one-half beam. By applying the technique to a calculation of the virial coefficient for a collection of flux carrying spin one-half particles, some severe obstacles to conventional views of the flux as a parameter which interpolates between bosonic and fermionic statistics are shown to occur. Although similar results for the scattering of arbitrary spin particles obtain in the Galilean limit, it is found that when spin one is considered in the context of a relativistic wave equation the singularity structure is too pathological to yield a consistent interpretation. The exact equivalence of the spin one-half Aharonov-Bohm effect to the Aharonov-Casher effect is also demonstrated and corresponding results for polarized beams are presented. Finally, it is shown that the Aharonov-Bohm effect for arbitrary spin in the Galilean limit is the exact solution in the two-particle sector of a Galilean covariant field theory.

The geometry of the N=2 superconformal manifolds is studied. It is shown that the underlying intrinsic operators of these manifolds form an N=2ℤ₂-graded algebra. We also show that the N=2 superconformal structure is equivalent to the Grassmann analyticity. Superconformal chiral tensors and integral measures are analyzed and the invariant superpotential, built of the primary chiral superfields, is given. A new realization of the N=2 supercurrent is obtained.

N=4 SU(2) conformal invariance is studied in the harmonic superspace. It is shown that the N=4 SU(2) conformal structure is equivalent to the harmonic analyticity. The solutions to the superconformal constraints are worked out in detail and the conformal properties of all objects of interest are given. A realization of the N=4 current in terms of the free (F.S.) hypermultiplet is obtained.

A regularization of the fermion determinant is discussed within a four-dimensional counterpart of the canonical dimensional regularization developed recently. The γ₅ anomaly is obtained and compared with those obtained within other regularization schemes. The equivalence with the ζ function regularization as well as the Fujikawa regularizations is shown. As a byproduct a Fujikawa regulator for the canonical dimensional regularization is constructed.

-invariant conformal field theories admit perturbations preserving integrability and leading to massive quantum field theories. The unitary and crossing-invariant S matrices of such QFTs are explicitly constructed by restricting the SL(n, q)-symmetric solutions of the Yang-Baxter equations when q^n+k=1. These scattering theories possess level-rank duality (n↔k).

Yang-Mills theory in conformal (essentially nonlocal) gauge is considered. This gauge is expressed in a local form by means of two auxiliary scalar fields. By the use of the BRST symmetry, the Slavnov-Taylor identities are obtained. These identities are applied to prove the renormalizability of the theory as well as to investigate the structure of the radiative corrections to the two-point vertex functions. It is shown that here a new class of conformal anomalies arises, connected with the absence of radiative corrections to the propagators including auxiliary fields.

The existence of a solution to generating equations for the effective gauge algebra with Abelian conversion of second-class constraints is established. The characteristic arbitrariness of this solution with given initial Hamiltonian and constraints is also studied.

We discuss, in the SL(2) Wess-Zumino-Novikov-Witten model, the quantum exchange relations for chiral vertex operators with arbitrary spin by using a free-field realization. We give a recursion formula for the monodromy matrices and the solution explicitly. They coincide with the q-6j symbol of the relevant quantum group U_q(sl(2)).

We review the current status of the determination of the quark mixing angles |V_qq′|, where q=u, c; q′=d, s, b. We consider essentially exclusive decay processes, taking into account the main sources of uncertainties, the available calculations of flavor symmetry breaking for hadronic matrix elements and the possibilities of improvement offered by new experimental results.

In some cases we provide full expressions for |V_qq′| in terms of measurable decay properties, which can be useful for new experimental data. Finally, we discuss briefly the effects on the unitarity tests of the Cabibbo-Kobayashi-Maskawa matrix when we consider recent corrections to the determination of |V_ud|.