International Journal of Modern Physics A

We reconsider the possibility that a new Q = −1/3, vector-like, isosinglet quark, h, which can appear in superstring-inspired E₆ models, may have appreciable mixing with the usual bottom (b) quark. Using the most recent data on the Kobayashi-Maskawa mixing matrix, ∊, ∊′/∊, , and mixing, we analyze the influence of h on rare processes, e.g., , b → sγ, and D → μ⁺μ⁻.

Recently we reported a successful fitting of the kinematic predictions of the Mass Theory of 5-dimensional Conformal Relativity to the Hadron Spectra. We use results obtained there to study the dynamical properties of the trilinear boson-matter interaction Lagrangian implied by isospin SU(2) gauge invariance. The isovector massive gauge boson allows for two interpretations: a J = 1 field and the 5-D derivative of a J = 0 field. We construct the Feynman Graphs for the ΠNN-interaction and show that (1) any given graph is actually an infinite sum of similar graphs, one for each member of the Conformal Family Field of the virtual Hadron and (2) that the individual coupling of each of these members depends on its mass, giving rise to an effectively energy-dependent coupling. Based on these features, we speculate on the interesting possibility that Perturbation Theory may be usable for hadron processes and calculate the matrix elements for a simplified model of pπ⁰ → pπ⁰ to second order. Useful comparisons are made with the analogous treatment in ordinary QFT.

We consider the construction of the N-string g-loop vertex for the bosonic string. The sewing procedure of Ref. 1, based on path integrals, is reformulated in terms of operators. This makes it trivial to demonstrate complete equivalence with the oscillator approach of Refs. 2, 3, and 4. Also, the equivalence of two very different loop-sewing procedures for the g-loop vacuum diagram can be demonstrated, this being a very strong indication that the formalism is completely independent of the sewing procedure even in the case of loops.

An exactly solvable two-dimensional model of Fateev and Zamolodchikov is shown to approach, in a certain limit, the standard XY-model at zero temperature. This model may be of some relevance to strings (and to knot theory perhaps).

In this paper, we explore the consequences of diffeomorphism invariance in generally covariant theories. Such theories in two and three dimensions are known to admit topological excitations called geons. It is shown by specific examples that a quantum state of two identical geons may not be an eigenstate of the geon exchange operator, which means that a geon may have no definite statistics. As shown before by Sorkin and as discussed further here, it may also happen, for instance, that in 3 + 1 dimensions a tensorial (spinorial) geon obeys Fermi (Bose) statistics, while in 2 + 1 dimensions an "integral-spin" geon can obey "fractional statistics". Thus ideas on spin and statistics borrowed from Poincaré invariant theories are not always valid in quantum gravity, at least without further physical inputs. Previously, it was shown by Friedman and Sorkin that pure gravity in three space dimensions may admit spinorial states. This result is extended to two dimensions where pure gravity is shown to admit "fractional spin" geons.

The affine extension of supergravity is investigated. We discuss only the loop algebra since the affine extension of the super-Poincaré algebra appears inconsistent. The construction of the affine supergravity theory has been carried out by the group manifold method and leads to an action describing infinite towers of gravitons and gravitinos that interact subject to the symmetries of the loop algebra. The equations of motion satisfy the usual consistency check.

Space-time decomposition of the Hilbert-Palatini action, written in a form which admits degenerate metrics, is considered. Simple numerology shows why D = 3 and 4 are singled out as admitting a simple phase space. The canonical structure of the degenerate sector turns out to be awkward. However, the real degenerate metrics obtained as solutions are the same as those that occur in Ashtekar's formulation of complex general relativity. An exact solution of Ashtekar's equations, with degenerate metric, shows that the manifestly four-dimensional form of the action, and its 3 + 1 form, are not quite equivalent.

We found the temperature at which the electroweak baryon-number nonconserving processes are frozen, as a function of the fermion number density of the universe, which results in the increase of the freezing temperature with the growth of the fermion number density combination . We combine this result with the Affleck-Dine baryogenesis mechanism to suggest a possible scenario for the evolution of the post-inflationary universe, according to which the universe could have passed through a hot stage with large baryon and lepton asymmetries , that are later erased at relatively low temperatures, the correct observational baryon asymmetry n_B/n_γ ~ 10⁻⁹ being finally produced.

The one-loop partition functions of the superconformal Thirring model for first order b − c and β − γ ghost fields are studied for both closed and open string boundary conditions. Bosonized partition functions are given by formal series which usually diverge because the energy spectrum of the theory is unbounded below as a correlate of nonunitarity. However, the same partition functions are then calculated by path integral methods directly in the fermionic formulation, and well-defined (convergent) integral representations are obtained. A formal series expansion of those integrals reproduces the bosonized partition functions.

The spectroscopic properties of the charmonium (Ψ) and bottomium (ϒ) families have been studied in the framework of the statistical model. The energy splittings of the S, P, D levels of Ψ and ϒ-families have been investigated using one-gluon exchange potential containing the running coupling constant, as a perturbation over the already existing confinement type of potentials. Our computed results are found to be in reasonably good agreement with the corresponding experimental findings and/or other theoretical estimates.

Multihadron rapidity distributions exhibit highly irregular (perhaps fractal) event structure. Application of methods used in nonlinear dynamics to hadronic data is made uncertain by the relatively small number of particles in a given event. We analyze three standard methods to assess their applicability: the Hausdorff (box-counting) method, the correlation dimension, and the information dimension. The Hausdorff method can work for large multiplicities if the fractal set (strange attractor) has simple self-similar behavior. It is noted that addition of points from different events will doubtless erase sponge-like structure characteristic of the attractor. This defect is even greater for the information dimension, whose proper definition requires probabilities whose evaluation involves event averaging. For a fixed attractor, this is of no consequence; however, individual collisions differ by a "noise" effect. The correlation dimension, which has the merit of rapid computational convergence, depends only on relative rapidities |y_i − y_j| and therefore should not depend on overall rapidity shifts between events. Possible statistical independence of different subsets of a given partition of n particles is analyzed using factorial cumulant moments and information entropy. Additivity of constituent cumulants and entropies is characteristic of statistical independence. Conditional entropies are introduced and used to generalize conventional definitions of information entropy and its (Renyi) generalization.