International Journal of Modern Physics A

This review is the full version of an invited contribution to the session on heavy-ion collisions at the Singapore Conference, where several topical points were discussed in detail, through a series of talks.

Results of a search for the pair production of charged heavy leptons in e⁺e⁻ annihilations over the center-of-mass energy range of 50 to 60.8 GeV are reported. We assume that the leptons are of the sequential type but have allowed for the case where the associated neutrino might be massive. Separate searches for evidence for decays to hadronic and leptonic final states, searches specialized for the case where the charged lepton and its associated neutrino are close in mass, and a search for stable heavy leptons have uncovered no evidence for the production of such particles at these energies. Mass limits for heavy leptons and their associated neutrinos are determined for a range of hadronic and leptonic decay branching fractions. A sequential charged heavy lepton with mass between 12.6 and 29.6 GeV/c² and with massless neutrino is excluded at the 95% confidence level.

By making use of the hidden connection between the [ℤ_N] parafermionic models and the [W_N]^p=N+1 nonlinearly extended conformal models, we show that the parafermionic descendants of the identity define, up to null currents, a W_N algebra. We discuss the essential features of this “parafermionic” W_N algebra, as well as the characterization of the parafermionic primary fields as W_N-invariant fields. Furthermore, we show that this W_N algebra can be represented, for generic values of N, in terms of only two free bosonic fields. Such a representation turns out to interpolate between two-boson representations of the W₃ and the W_∞ algebra known in the literature.

We study vortex solutions in the Born-Infeld theory coupled with a complex scalar field. We show that for a specific form of the “Higgs” potential the vortex satisfies a set of Bogomol’nyi-type equations. Another model, with nonlinear interaction between gauge and Higgs fields, is also considered. We show how it is derived from a supersymmetric extension of the Born-Infeld theory with a minimally coupled complex scalar field.

We investigate the use of renormalization group transformations (RGTs) to define an effective colour dielectric theory on the lattice. Starting from the pure gauge sector of SU(2), we try to find an optimal RGT which leads to an effective action with few parameters. We test this effective action by simulating the colour dielectric theory on the lattice and checking for operator matching.

A Bethe-Salpeter equation (BSE) has been derived using a covariant confining interaction motivated from QCD. Recently, this interaction has been applied to a qqq system under the null plane ansatz (NPA), which reduces the resulting equations to three-dimensional form. For equal mass quarks, encouraging results were obtained for baryon masses and quantum numbers. In the present paper, this formalism is generalized to unequal mass kinematics and applied to the spectroscopy of strange baryons (Λ, Σ, Ξ, Ω). All input parameters are fixed from previous calculations. The reduced qqq equation in the NPA is solved algebraically in a six-dimensional harmonic oscillator basis, on lines analogous to the corresponding techniques developed for the equal mass qqq problem. The results on the Λ, Σ spectra are in good agreement with data, where available, up to levels N=5. Our results are compared with those from another relativized potential of baryon masses.

We review stochastic inflation and its consequences for the interpretation of wave functions in quantum cosmology.

Some issues in the quantum mechanics of gravitational collapse are discussed in the framework of a simple minisuperspace model, consisting of a Friedman metric coupled to a massless scalar field. The model illustrates the role of intrinsic time coordinates in parametrizing gravitational collapse through a singularity, and the relevance of quantizing the metric scale factor over an infinite, rather than half-infinite, range.

We investigate the implications of CP violation from new physics for the process using transversely polarized electrons at SLC and LEP. We define an asymmetry whose nonzero value signals the time reversal violation of the underlying interactions. Using a general effective Lagrangian we analyse the signal expected from any new physics. We show that for a large class of theories this observable is exclusively sensitive to a single CP-violating electron gauge boson dimension six interaction. Experiments at LEP can probe such CP violation from new physics at scales up to several TeV.

We describe a method of generating a family of supersymmetric quantum mechanics models depending on two positive integers (l,j), l>j. All of them exhibit singular superpotentials, explicit breaking of supersymmetry, a normalizable zero mode and j eigenstates with negative energy. We discuss the nodal structure of the solutions to the two supersymmetric partner Schrödinger equations. If we fix j=1, the two Hamiltonians H₋ and H₊ include Pöschl-Teller potentials and under these circumstances the problem is solvable. Maintaining j=1, but now letting l ∈ (−∞, ∞), we find a model similar to the ones which have been considered in the literature.

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.