Modern Physics Letters A

We briefly review some selected topics in the small x physics. In particular, we discuss the progress in the problem related to the resummation at small x and the parton saturation phenomena. Finally we discuss some phenomenological applications to deep inelastic scattering, hadron and heavy ion collisions.

We study Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on SL(2, R) within the AKNS framework, this model is based on SL(2, R)⊗U(1). The connection between the scalar and the matrix descriptions in this case implies that the generic Darboux matrix for the TB hierarchy has a different structure from that in the models based on SL(2, R) studied thus far. The conventional Darboux transformation is shown to be quite restricted in this model. We construct a modified Darboux transformation which has a much richer structure and which also allows for multi-soliton solutions to be written in terms of Wronskians. Using the modified Darboux transformations, we explicitly construct one-soliton/kink solutions for the model.

We study a gauged Chern–Simons–CP(1) system. We show that contrary to previous claims, the model in the absence of a potential term cannot support finite size soliton solution in R².

The paper deals with a spatially homogeneous and anisotropic universe filled with perfect fluid and dark energy components. The two sources are assumed to interact minimally together with a special law of variation for the average Hubble's parameter in order to solve the Einstein's field equations. The law yields two explicit forms of the scale factor governing the Bianchi-V spacetime and constant values of deceleration parameter. The role of dark energy with variable equation of state parameter has been studied in detail in the evolution of Bianchi-V universe. It has been found that dark energy dominates the universe at the present epoch, which is consistent with the observations. The universe achieves flatness after the dominance of dark energy. The physical behavior of the universe has been discussed in detail.

We propose a universal mixing hypothesis between quark and lepton sectors at high energy scale (probably GUT scale) where quark–lepton universality holds. Namely in the charged lepton diagonal base, all the other mass matrices for up and down quarks and neutrinos are diagonalized by the same unitary matrix except for the phase elements. Thanks to this hypothesis, the observed values of the Cabibbo–Kobayashi–Maskawa (CKM) quark mixing matrix and the mixing angles θ₁₂ and θ₂₃ in the Maki–Nakagawa–Sakata (MNS) lepton mixing matrix can predict the unknown magnitudes of the mixing angle θ₁₃ and of the CP violating Dirac phase δ in the MNS matrix. Their allowed regions are rather narrow, 0.036 < sin θ₁₃ < 0.048 and 6° < δ < 12°.

The Casimir effect for a massless scalar field on the helix boundary condition which is named as quantum spring is studied in our recent paper.²⁷ Here, the Casimir effect of the quantum spring is investigated in (D+1)-dimensional spacetime for the massless and massive scalar fields by using the zeta function techniques. We obtain the exact results of the Casimir energy and Casimir force for any D, which indicate a Z₂ symmetry of the two space dimensions. The Casimir energy and Casimir force have different expressions for odd and even dimensional space in the massless case but in both cases the force is attractive. In the case of odd-dimensional space, the Casimir energy density can be expressed by the Bernoulli numbers, while in the even case it can be expressed by the ζ-function. And we also show that the Casimir force has a maximum value which depends on the spacetime dimensions. In particular, for a massive scalar field, we found that the Casimir force varies as the mass of the field changes.

Information measures for relativistic quantum spinors are constructed to satisfy various postulated properties such as normalization invariance and positivity. Those measures are then used to motivate generalized Lagrangians meant to probe shorter distance physics within the maximum uncertainty framework. The modified evolution equations that follow are necessarily nonlinear and simultaneously violate Lorentz invariance, supporting previous heuristic arguments linking quantum nonlinearity with Lorentz violation. The nonlinear equations also break discrete symmetries. We discuss the implications of our results for physics in the neutrino sector and cosmology.