International Journal of Modern Physics A

Top-quark production is observed in collisions at at the Fermilab Tevatron. The CDF and DØ collaborations observe signals consistent with to but inconsistent with the background prediction by 4.8σ (CDF) and 4.6σ (DØ). Additional evidence for the top quark is provided by a peak in the reconstructed mass distribution. The kinematic properties of the excess events are consistent with the top-quark decay. The top-quark mass has been measured to be 176±8(stat.) ±10(sys.)GeV/c² (CDF) and ±22(sys.)GeV/c² (DØ), and the -production cross section to be and 6.4±2.2 pb (DØ).

The notions of ordinary, covariant and Lie differentials are considered as operators over differentiable manifolds with different (not only by sign) contravariant and covariant affine connections and metric. The difference between the interpretations of the ordinary differential as a covariant basic vector field and as a component of a contravariant vector field is discussed. By means of the covariant metric and the ordinary differential the notion of the line element is introduced and the geodesic equation is obtained and compared with the autoparallel equation.

The Regge trajectories of a charged string in a magnetic background are derived by using a decomposition of the rest energy in terms of the Casimir operators of the theory. The first Regge trajectory is given by a family of infinitely many parallel straight lines, one for each spin projection along the magnetic field. Using the trajectories linking rest energy and spin, a critical magnetic field is found, for each spin value, at which the correspondent spin state with the highest spin projection becomes massless.

We give a simple diagrammatic algorithm for writing the chiral large N expansion of intersecting Wilson loops in 2D SU(N) and U(N) Yang-Mills theory in terms of symmetric groups, generalizing the result of Gross and Taylor for partition functions. We prove that these expansions compute Euler characters of a space of branched covering maps from string worldsheets with boundaries. We prove that the Migdal-Makeenko equations hold for the chiral theory and show that they can be expressed as linear constraints on perturbations of the chiral YM₂ partition functions. We briefly discuss finite N, the nonchiral expansion, and higher-dimensional lattice models.

The problem of calculating the mass spectrum of the two-body Bethe-Salpeter equation is studied with no reduction to the three-dimensional (“quasipotential”) equation. The method to find the ground state and excited states for a channel with any quantum numbers is presented. The problem of the confining interaction for the Bethe-Salpeter equation is discussed from the point of view of formal properties of the bound state spectrum, but with only inspiration from QCD. We study the kernel that is nonvanishing at large Euclidean intervals, i.e. R_E→∞, which is constructed as a special limiting case of the sum of the covariant one-boson-exchange kernels. In the coordinate space this kernel is just a positive constant and corresponds to the kernel ∝ δ(k_E) in the momentum space. When the usual attractive interaction is added, it is found that this kernel is similar in its effect to the nonrelativistic potential in coordinate space, V(r), with V(r→∞)→V_∞. The positive real constant V_∞ gives the scale that defines the limit of the bound state spectrum compared to the sum of the constituent masses, M < 2m+V_∞. At the same time, the self-energy corrections remove the singularities from the propagators of the constituents, i.e. constituents do not propagate as free particles. The combination of these features of the solutions allows an interpretation of this type of interaction as a confining one. The illustrative analytical and numerical calculations are presented for a model of massive scalar particles with scalar interaction, i.e. the “massive Wick model.”

We study the λɸ⁴ field theory in a flat Robertson-Walker space-time using the functional Schrödinger picture. We introduce a simple Gaussian approximation to analyze the time evolution of pure states and we establish the renormalizability of the approximation. We also show that the energy–momentum tensor in this approximation is finite once we consider the usual mass and coupling constant renormalizations.

We develop a relativistic free wave equation on the complexified quaternions, linear in the derivatives. Even if the wave functions are only one-component, we show that four independent solutions, corresponding to those of the Dirac equation, exist. A partial set of translations between complex and complexified quaternionic quantum mechanics may be defined.

The overlap formulation is applied to calculate the chiral determinant on a two-dimensional torus with twisted boundary conditions. We first evaluate the continuum overlap, which is convergent and well-defined, and yields the correct string theory result for both the real and imaginary parts of the effective action. We then show that the lattice version of the overlap gives the continuum overlap results in the limit where the lattice spacing tends to zero, and that the subleading terms in that limit are irrelevant.

We study the effects of spatial curvature on classical and quantum string dynamics. We find the general solution of the circular string motion in static Robertson–Walker space-times with closed or open sections. This is given closely and completely in terms of elliptic functions. The physical properties, string length, energy and pressure are computed and analyzed. We find the back-reaction effect of these strings on the space-time: the self-consistent solution to the Einstein equations is a spatially closed (K>0) space-time with a selected value of the curvature index K (the scale factor is normalized to unity). No self-consistent solutions with K≤0 exist. We semiclassically quantize the circular strings and find the mass m in each case. For K>0, the very massive strings, oscillating on the full hypersphere, have m²~Kn²(n∈N₀)independent of α' and the level spacing grows with n, while the strings oscillating on one hemisphere (without crossing the equator) have m²α′~n and a finite number of states N~1/Kα′. For K<0, there are infinitely many string states with masses m log m ~ n, i.e. the level spacing grows slower than n.

The stationary string solutions as well as the generic string fluctuations around the center of mass are also found and analyzed in closed form.