International Journal of Modern Physics A

We investigate the gravitational collapsing phenomenon in the spherically symmetric Einstein–Maxwell-dilaton system with a positive cosmological constant. As a preparation, we first study some general properties of the horizons in asymptotically de Sitter space–time and prove that the area of the horizons does not decrease and has an upper bound if the matter fields satisfy the dominant energy condition. By using these results, we analytically show that once gravitational collapse occurs from any initial data on a null hypersurface, the system of field equations breaks down inevitably in the domain of outer communications or the boundary, i.e. the black hole event horizon provided that a future null infinity ℐ⁺ exists, or the asymptotic structure at ℐ⁺ is broken and the universe will recollapse. In order to clarify which history does the universe trace, we perform a numerical simulation. Then, the dilaton field diverges faster than the logarithmic function almost uniformly and the asymptotic structure would be broken. This implies that the cosmic no hair conjecture is violated in the generalized theory of gravity.

The Hopf algebra of Feynman diagrams, analyzed by A. Connes and D. Kreimer, is considered from the perspective of the theory of effective actions and generalized τ-functions, which describes the action of diffeomorphism and shift groups in the moduli space of coupling constants. These considerations provide additional evidence of the hidden group (integrable) structure behind the standard formalism of quantum field theory.

We study the 19-vertex model associated with the quantum group at critical regime |q|=1. We give the realizations of the vertex operators in terms of free bosons and free fermions. Using these free field realizations, we present integral representations for the correlation functions.

A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and the quasiexactly-solvable anharmonic oscillators are found. They can be viewed as a translation-covariant discretization of the (an)harmonic oscillator preserving isospectrality. The notion of the q-deformation of the canonical equivalence leading to a dilatation-covariant discretization preserving polynomiality of eigenfunctions is also presented.

K→ππ, K_L-K_S mass difference (Δ m_K) and K_L→γγ^(*) are studied systematically by decomposing their amplitude into a sum of factorizable and nonfactorizable ones. The former is calculated by using the naive factorization while the latter is assumed to be controlled by hadron dynamics. Nonfactorizable amplitudes for the K→ππ decays which are estimated by using a hard pion technique dominates the |ΔI| = ½ amplitude. It is seen that the naively factorized short distance term dominates Δm_K as usual since contributions of pseudoscalar-meson poles and ππ intermediate states as the nonfactorizable long distance effects interfere destructively with each other. The K*-meson pole survives in the K_L→γγ decay and plays an important role in the present perspective in contrast with the existing theories which are restricted by the theory of field algebra. The form factor for the Dalitz decays of K_L and their rates are compared with the existing data.

We discuss the confining features of the Schwinger model on the Poincaré half plane. We show that despite the fact that the expectation value of the large Wilson loop of massless Schwinger model displays perimeter behavior, the system can be in confining phase due to the singularity of the metric at horizontal axis. It is also shown that in the quenched Schwinger model, the area dependence of the Wilson loop, in contrast to the flat case, is a not a sign of confinement and the model has a finite energy even for large external charges separation. The presence of dynamical fermions cannot modify the screening or the confining behavior of the system. Finally we show that in the massive Schwinger model, the system is again in screening phase. The zero curvature limit of the solutions is also discussed.

The CKM-matrix V is written as a linear combination of the unit matrix I and a matrix U which causes intergenerational-mixing. It is shown that such a V results from a class of quark-mass matrices. The matrix U has to be Hermitian and unitary and therefore can depend at most on four real parameters. The available data on the CKM-matrix including CP-violation can be reproduced by . This is also true for the special case when U depends on only 2 real parameters. Also, for such a V the invariant phase Φ≡ϕ₁₂+ϕ₂₃-ϕ₁₃, satisfies a criterion suggested for "maximal" CP-violation.