Modern Physics Letters A

We propose a new cosmological model with a time-dependent cosmological constant (Λ∝1/t²), which starting at the Planck time as , evolves to the present-day allowed value of . This scenario is supported by noncritical string theory considerations. We compute the age of the Universe and the time dependence of the scale factor in this model, and find general agreement with recent determinations of the Hubble parameter for substantial values of Ω_Λ. This effectively low-density open Universe model differs from the traditional cosmological constant model, and has observable implications for particle physics and cosmology.

A two-dimensional string effective action is obtained by dimensionally reducing the bosonic part of the 10-dimensional heterotic string effective action. It is shown that this effective action, with a few restrictions on some backgrounds, describes a two-dimensional model which admits an infinite sequence of nonlocal conserved currents.

We derive a simple calculation rule for Aoyama-Tamra’s prescription for path integral with degenerated potential minima. Nonperturbative corrections due to the restricted functional space (fundamental region) can systematically be computed with this rule. It becomes manifest that the prescription might give Borel summable series for finite temperature (or volume) system with quantum tunneling, while the advantage is lost at zero temperature (or infinite volume) limit.

Processes of heavy quark photoproduction at HERA energies and beyond are investigated using the semihard (k_⊥ factorization) approach. Virtuality and longitudinal polarization of gluons in the photon-gluon subprocess as well as the saturation effects in the gluon distribution function at small x have been taken into account. The total cross-sections, rapidity and p_⊥ distributions of the charm and beauty quark photoproduction have been calculated. The results are compared with ZEUS experimental data for charm photoproduction cross-section.

A representation of one-parameter deformation of U(1) Kac-Moody and Virasoro algebras is obtained throughout the infinite matrix algebra ā_∞. Their central extensions are also investigated.

The instanton configuration in the SU(2)-gauge system with a Higgs doublet is constructed by using the new valley method. This method defines the configuration by an extension of the field equation and allows the exact conversion of the quasi-zero eigen-mode to a collective coordinate. It does not require ad hoc constraints used in the current constrained instanton method and provides a better mathematical formalism than the constrained instanton method. The resulting instanton, which we call “valley instanton”, is shown to have the desirable behaviors. The result of the numerical investigation is also presented.

We propose a new way for describing the transition between two quantum Hall effect states with different filling factors within the framework of rational conformal field theory. Using a particular class of nonunitary theories, we explicitly recover Jain’s picture of attaching flux quanta by the fusion rules of primary fields. Filling higher Landau levels of composite fermions can be described by taking tensor products of conformal theories. The usual projection to the lowest Landau level corresponds then to a simple coset of these tensor products with several U(1)-theories divided out. These two operations — the fusion map and the tensor map — can explain the Jain series and all other observed fractions as exceptional cases. Within our scheme of transitions we naturally find a field with the experimentally observed universal critical exponent 7/3.

The problem of a harmonic oscillator coupling to an electromagnetic potential plus a topological-like (Chern-Simons) massive term, in two-dimensional space, is studied in the light of the symplectic formalism proposed by Faddeev and Jackiw for constrained systems.