International Journal of Modern Physics A

General properties of the τ leptons are reviewed using the recent measurements of production and decay of τ leptons. The improvements in the knowledge of the τ mass and the limits on ν_τ mass are reported. New improved measurements of the τ polarization and asymmetries performed at LEP and SLC prove a measurement of the axial and vector part of the neutral current at the per mil level. For the leptonic charged current, no deviation from the V–A Lorentz structure of the current is observed. Improvements on the lifetime and leptonic branching fractions allow a check of the charged current universality at the 0.5% level. New hadronic decay channels have been measured, mainly those involving kaons and η mesons. A precise determination of α_s at the τ mass energy scale is performed. Finally, tests of possible new physics beyond the Standard Model are discussed.

We construct two solutions of the minimally coupled Einstein-scalar field equations, representing regular deformations of Schwarzschild black holes by a self-interacting, static, scalar field. One solution features an exponentially decaying scalar field and a triple-well interaction potential; the other one is completely analytic and sprouts Coulomb-like scalar hair. Both evade the no-hair theorem by having partially negative potential, in conflict with the dominant energy condition. The linear perturbation theory around such backgrounds is developed in general, and yields stability criteria in terms of effective potentials for an analog Schrödinger problem. We can test for more than half of the perturbation modes, and our solutions prove to be stable against those.

We show that the Abelian Proca model, which is gauge noninvariant with second class constraints can be converted into gauge theories with first class constraints. The method used, which we call gauge unfixing, employs a projection operator defined in the original phase space. This operator can be constructed in more than one way and so we get more than one gauge theory. Two such gauge theories are the Stückelberg theory and the theory of Maxwell field interacting with an antisymmetric tensor field. We also show that the application of the projection operator does not affect the Lorentz invariance of this model.

N=(0,2) heterotic string theories on Calabi–Yau spaces are considered based on linear sigma approaches. We construct (0,2) sigma models on complete intersection Calabi–Yau spaces, ℳ, realized in a product of weighted projective spaces. The definition of the associating vector bundle V over ℳ is given. These models are formulated as the IR limits of (0,2) U(1)^N gauged linear sigma models. Examining their phase structures, we observe that there are hybrid phases where one cannot intrinsically distinguish between the defining polynomials of the Calabi–Yau space ℳ and those of the gauge bundle V. Thus we construct dual pairs of two (0,2) Calabi–Yau sigma models which are isomorphic in their hybrid phases. In addition, generalizing the gauge bundle into the direct sum of bundles, we study the duality of (0,2) string vacua.

Evens et al.¹ have given a gauge-invariant regularization scheme for QED which they have named nonlocal regularization. The present authors² have worked out the QED vertex part in this scheme of regularization. In this paper we present a Ward identity for nonlocal QED to the order of two loops (order e⁴). In the limit of QED (Λ→∞), this identity reduces to the usual form of the Ward identity.

We discuss the unitarity relation of the Aharonov–Bohm scattering amplitude with the hope that it distinguishes between the differing treatment which employ different incident waves. We find that the original Aharonov–Bohm scattering amplitude satisfies the unitarity relation under the regularization prescription whose theoretical foundation does not appear to be understood. On the other land, the amplitude obtained by Ruijsenaars who uses plane wave as incident wave also satisfies the unitarity relation but in an unusual way.

Using a description of defects in solids in terms of three-dimensional gravity, we study the propagation of electrons in the background of disclinations and screw dislocations. We study the situations where there are bound states that are effectively localized on the defect and hence can be described in terms of an effective (1+1)-dimensional field theory for the low energy excitations. In the case of screw dislocations, we find that these excitations are chiral and can be described by an effective field theory of chiral fermions. Fermions of both chirality occur even for a given direction of the magnetic field. The "net" chirality of the system however is not always the same for a given direction of the magnetic field, but changes from one sign of the chirality through zero to the other sign as the Fermi momentum or the magnitude of the magnetic flux is varied. On coupling to an external electromagnetic field, the latter becomes anomalous and predicts novels conduction properties for these material.