International Journal of Modern Physics A

This paper reviews the most recent results from LEP and the Tevatron on production rates, masses and widths of orbitally excited B meson states. It also provides possible explanations for the various discrepancies observed between some of these experimental results.

We consider the quantum mechanical notion of the geometrical (Berry) phase in SU(2) gauge theory, both in the continuum and on the lattice. It is shown that in the coherent state basis eigenvalues of the Wilson loop operator naturally decompose into the geometrical and dynamical phase factors. Moreover, for each Wilson loop there is a unique choice of U(1) gauge rotations which do not change the value of the Berry phase. Determining this U(1) locally in terms of infinitesimal Wilson loops we define monopole-like defects and study their properties in numerical simulations on the lattice. The construction is gauge dependent, as is common for all known definitions of monopoles. We argue that for physical applications the use of the Lorentz gauge is most appropriate. And, indeed, the constructed monopoles have the correct continuum limit in this gauge. Physical consequences are briefly discussed.

A dual form of (3+1)-dimensional Yang–Mills theory is obtained as another SO(3) gauge theory. Duality transformation is realized as a canonical transformation. The non-Abelian Gauss law implies the corresponding Gauss law for the dual theory. The dual theory is nonlocal. There is a nonlocal version of Yang–Mills theory which is self-dual.

In the Cold Dark Matter (hereafter CDM) scenario even isolated density peaks contain a high fraction of small scale clumps having velocities larger than the average escape velocity from the structure. These clumps populate protoclusters, especially in the peripheral regions, r≥R_f (where R_f is the filtering scale). During the cluster collapse and the subsequent secondary infall, collapsing or infalling clumps (having v<v_esc) interact with the quoted unboundclumps (or high speed clumps, as we also call them) having v>v_esc. We study the interaction between these two kinds of clumps by means of the impulse approximation¹ and we find that the collapse of bound clumps is accelerated with respect to the homogeneous case (Gunn and Gott's model, Ref. 2). The acceleration of the collapse increases with decreasing height of the peak, ν. We finally compare the acceleration produced by this effect to the slowing down effect produced by the gravitational interaction of the quadrupole moment of the system with the tidal field of the matter of the neighboring proto-clusters studied by Del Popolo and Gambera.³ We find that the magnitude of the slowing down effect is larger than the acceleration produced by the effect studied in this paper, only in the outskirts of the cluster. We want to stress that the one which we study in this paper is also present in an isolated protocluster, being produced by the interaction of the collapsing clumps with the unbound substructure internal to the collapsing clumps itself while that studied in Ref. 3 is produced by substructure external to the density peak.

In this paper we consider the scalar sector of Duffin–Kemmer–Petiau theory in the framework of Epstein–Glaser causal method. We calculate the lowest order distributions for Compton scattering, vacuum polarization, self-energy and vertex corrections. By requiring gauge invariance of the theory we recover, in a natural way, the scalar propagator of the usual effective theory.

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one and is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it the Hilbert space of a quantum system (from conventional quantum mechanics) is replaced with an appropriate Hilbert bundle of states and a pure state of the system is described by a lifting of paths or section along paths in this bundle. The evolution of a pure state is determined through the bundle (analog of the) Schrödinger equation. Now the dynamical variables and density operators are described via liftings of paths or morphisms along paths in suitable bundles. The mentioned quantities are connected by a number of relations derived in this work.

The present fourth part of this series is devoted mainly to the fibre bundle description of mixed quantum states. We show that to the conventional density operator there corresponds a unique density lifting of paths for which the corresponding equations of motion are derived. It is also investigated the bundle description of mixed quantum states in the different pictures of motion. We calculate the curvature of the evolution transport and prove that it is curvature free iff the values of the Hamiltonian operator at different moments commute.

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one and is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it the Hilbert space of a quantum system (from conventional quantum mechanics) is replaced with an appropriate Hilbert bundle of states and a pure state of the system is described by a lifting of paths or section along paths in this bundle. The evolution of a pure state is determined through the bundle (analog of the) Schrödinger equation. Now the dynamical variables and density operator are described via liftings of paths or morphisms along paths in suitable bundles. The mentioned quantities are connected by a number of relations derived in this work.

This is the fifth, closing, part of our investigation. We briefly discuss the observer's role in the theory and different realizations of the space–time model used as a base space in the bundle approach to quantum mechanics. The exact conditions for the equivalence of Hilbert bundle and Hilbert space formulations of the theory are pointed out. A table of comparison between both descriptions of nonrelativistic quantum mechanics is presented. We discuss some principal moments of the Hilbert bundle description and show that as a scheme it is more general than the Hilbert space one. Different directions for further research are pointed out.

Exact coherent states in the Calogero–Sutherland models (of time-dependent parameters) which describe identical harmonic oscillators interacting through inverse-square potentials are constructed, in terms of the classical solutions of a harmonic oscillator. For quasi-periodic coherent states of the time-periodic systems, geometric phases are evaluated. For the A_N-1 Calogero–Sutherland model, the phase is calculated for a general coherent state. The phases for other models are also considered.

We discuss the impact of different measurements of the asymmetry in the extraction of parametrizations of parton distribution functions.

A new renormalization group method is used to calculate the photon propagator in the high four-momentum regime. The assumption that this propagator is a self-similar object leads directly to a functional equation of evolution involving an invariant charge (effective coupling function) which, in turn, is a functional of the propagator. Numerical results produced by this theory depend on a single unknown, namely, the scale in which the four-momentum k is measured. Calculations are presented for several values of this scale. From these it is concluded that the transverse photon propagator behaves asymptotically as D_⊥(k)~k^2(λ-1) with the value of λ (the anomalous dimension) falling in the range (0.12, 1).