International Journal of Modern Physics A

We show that a common evolutionary history can produce the black hole binaries in the Galaxy in which the black holes have masses of ~ 5 - 10M_⊙. In the black hole binaries with low-mass, ≲ 2.5M_⊙ ZAMS (zero age main sequence) companions, the latter remain in main sequence during the active stage of soft X-ray transients (SXT's), most of them being of K or M classification. In two intermediate cases, IL Lupi and Nova Scorpii with ZAMS ~ 2.5M_⊙ companions the orbits are greatly widened because of large mass loss in the explosion forming the black hole, and whereas these companions are in late main sequence evolution, they are close to evolving. Binaries with companion ZAMS masses ≳ 3M_⊙ are initially "silent" until the companion begins evolving across the Herzsprung gap.

We provide evidence that the narrower, shorter period binaries, with companions now in main sequence, are fossil remnants of gamma ray bursters (GRB's). We also show that the GRB is generally accompanied by a hypernova explosion (a very energetic supernova explosion). We further show that the binaries with evolved companions are good models for some of the ultraluminous X-ray sources (ULX's) recently seen by Chandra in other galaxies.

The great regularity in our evolutionary history, especially the fact that most of the companions of ZAMS mass ≲ 2.5M_⊙ remain in main sequences as K or M stars can be explained by the mass loss in common envelope evolution to be Case C; i.e. to occur only after core He burning has finished. Since our argument for Case C mass transfer is not generally understood in the community, we add an appendix, showing that with certain assumptions which we outline we can reproduce the regularities in the evolution of black hole binaries by Case C mass transfer.

Recently, the author has proposed a generalization of the matrix and vector models approach to the theory of random surfaces and polymers. The idea is to replace the simple matrix or vector (path)-integrals by gauge theory or nonlinear σ model (path)-integrals. We explain how this solves one of the most fundamental limitations of the classic approach: we automatically obtain nonperturbative definitions in non-Borel summable cases. This is exemplified in the simplest possible examples involving O(N) symmetric nonlinear σ models with N-dimensional target spaces, for which we construct (multi)critical metrics. The nonperturbative definitions of the double scaled, manifestly positive, partition functions rely on remarkable identities involving (path)-integrals.

Evolution of structure functions and their moments at low and moderate Q² is studied in the chiral field theory. Evolution equations based on perturbation expansion in the coupling constant of the effective theory are derived and solved for the moments. The kernels of evolution arising from different processes have been calculated with contributions from direct and cross channels, the interference terms being non-negligible in the kinematic regions under consideration. This is shown to lead to flavor-dependence of the kernels which manifests in observable effects. The invalidity of the probabilistic approach to the evolution process is also pointed out.

Representation of the algebra of FP (anti)ghosts in string theory is studied by generalizing the recursive fermion system in the Cuntz algebra constructed previously. For that purpose, the pseudo-Cuntz algebra, which is a *-algebra generalizing the Cuntz algebra and acting on indefinite-metric vector spaces, is introduced. The algebra of FP (anti)ghosts in string theory is embedded into the pseudo-Cuntz algebra recursively in two different ways. Restricting a certain permutation representation of the pseudo-Cuntz algebra, representations of these two recursive FP ghost systems are obtained. With respect to the zero-mode operators of FP (anti)ghosts, it is shown that one corresponds to the four-dimensional representation found recently by one of the present authors (M. Abe) and Nakanishi, while the other corresponds to the two-dimensional one by Kato and Ogawa.

We have examined the deformation of a generic non-Abelian gauge theory obtained by replacing its Lie group by the corresponding quantum group. This deformed gauge theory has more degrees of freedom than the theory from which it is derived. By going over from point particles in the standard theory to solitonic particles in the deformed theory, it is proposed that we interpret the new degrees of freedom as being descriptive of the non-locality of the deformed theory. It also turns out that the original Lie algebra gets replaced by two dual algebras, one of which lies close to and approaches the original Lie algebra in a correspondence limit, while the second algebra is new and disappears in this same correspondence limit. The exotic field particles associated with the second algebra can be interpreted as quark-like constituents of the solitons, which are themselves described as point particles in the first algebra. These ideas are explored for q-deformed SU(2) and GL_q(3).

We consider a generalized scalar–tensor theory, where we let the coupling function ω(ϕ) and the effective cosmological constants Λ(ϕ) be undetermined. We obtain general expressions for ω(ϕ) and Λ(ϕ) in terms of the scalar field and the scale factor, and show that ω(ϕ) depends on the scalar field and the scale factor in a complicated way. In order to study the conditions for an accelerated expansion at the present time and a decelerated expansion in the past, we assume a power law evolution for the scalar field and the scale factor. We analyze the required conditions that allow our model to satisfy the weak field limits on ω(ϕ), and at the same time, to obtain the correct values of cosmological parameters, as the energy density Ω_m0 and cosmological constant Λ(t₀). We also study the conditions for a decelerated expansion at an early time dominated by radiation. We find values for ω(ϕ) and Λ(ϕ) consistent with the expectations of a where the cosmological constant decreases with the time and the coupling function increases until the values are accepted today.

The multi-particle productions in neutrino–nucleon collisions at high energy are investigated through the analysis of the data of the experiment CERN-WA-025 at neutrino energy less than 260 GeV and the experiments FNAL-616 and FNAL-701 at energy range 120–250 GeV. The general features of these experiments are used as base to build a hypothetical model that views the reaction through a Feynman diagram of two vertices. The first of which concerns the weak interaction between the neutrino and the quark constituents of the nucleon. At the second vertex, a strong color field is assumed to play the role of particle production, which depend on the momentum transferred from the first vertex. The wave functions of the nucleon constituent quarks are determined using the variation method and relevant boundary conditions are applied to calculate the deep inelastic cross sections of the virtual diagram.