International Journal of Modern Physics A

Unlike some models whose relevance to Nature is still a big question mark, Quantum Chromodynamics (QCD) will stay with us forever. QCD, born in 1973, is a very rich theory supposed to describe the widest range of strong interaction phenomena: from nuclear physics to Regge behavior at large E, from color confinement to quark–gluon matter at high densities/temperatures (neutron stars); the vast horizons of the hadronic world: chiral dynamics, glueballs, exotics, light and heavy quarkonia and mixtures thereof, exclusive and inclusive phenomena, interplay between strong forces and weak interactions, etc. Efforts aimed at solving the underlying theory, QCD, continue. In a remarkable entanglement, theoretical constructions of the 1970's and 1990's combine with today's ideas based on holographic description and strong–weak coupling duality, to provide new insights and a deeper understanding.

We apply Bogolubov approach to QCD with two light quarks to demonstrate a spontaneous generation of an effective interaction, leading to the Nambu–Jona-Lasinio model. The resulting theory contains two parameters: average low-energy value of α_s and current light quark mass m₀. All other low-energy parameters: the pion decay constant, mass of the π-meson, mass of the σ-meson and its width, the constituent quark mass, and the quark condensate are expressed in terms of the two input parameters in satisfactory correspondence to experimental data and chiral phenomenology. For example, in the approximation being used we have for α_s = 0.67 and m₀ = 20 MeV: f_π = 93 MeV, m_π = 135 MeV, m_σ = 492 MeV, Γ_σ = 574 MeV, m_q = 295 MeV, .

Based on a large component QCD derived directly from full QCD by integrating over the small components of quark fields with |p| < E + m_Q, an alternative quantization procedure is adopted to establish a basic theoretical framework of heavy quark effective field theory (HQEFT) in the sense of effective quantum field theory. The procedure concerns quantum generators of Poincaré group, Hilbert and Fock space, anticommutations and velocity superselection rule, propagator and Feynman rules, finite mass corrections, trivialization of gluon couplings and renormalization of Wilson loop. The Lorentz invariance and discrete symmetries in HQEFT are explicitly illustrated. Some new symmetries in the infinite mass limit are discussed. Weak transition matrix elements and masses of hadrons in HQEFT are well defined to display a manifest spin-flavor symmetry and 1/m_Q corrections. A simple trace formulation approach is explicitly demonstrated by using LSZ reduction formula in HQEFT, and shown to be very useful for parametrizing the transition form factors via 1/m_Q expansion. As the heavy quark and antiquark fields in HQEFT are treated on the same footing in a fully symmetric way, the quark–antiquark coupling terms naturally appear and play important roles for simplifying the structure of transition matrix elements, and for understanding the introduction of "dressed heavy quark"–hadron duality. In the case that the "longitudinal" and "transverse" residual momenta of heavy quark are at the same order of power counting, HQEFT provides a consistent approach for systematically analyzing heavy quark expansion in terms of 1/m_Q. Some interesting features in applications of HQEFT to heavy hadron systems are briefly outlined.

Many approaches to a semiclassical description of gravity lead to an integer black hole entropy. In four dimensions this implies that the Schwarzschild radius obeys a formula which describes the distance covered by a Brownian random walk. For the higher-dimensional Schwarzschild–Tangherlini black hole, its radius relates similarly to a fractional Brownian walk. We propose a possible microscopic explanation for these random walk structures based on microscopic chains which fill the interior of the black hole.

The Darboux algorithm is applied to an exactly solvable one-dimensional stationary Dirac equation, with non-Hermitian, pseudoscalar interaction V₀(x). This generates a hierarchy of exactly solvable Dirac Hamiltonians, , defined by new non-Hermitian interactions V₁(x), which are also pseudoscalar. It is shown that are isospectral to the initial Hamiltonian h₀, except for certain missing states.

We have examined brane world solutions for the low energy effective string gravity action coupled with a quadratic dilaton potential in string frame. For a negative bulk cosmological constant, static 3-brane solutions exist. Their properties are analyzed depending on the quadratic potential parameters. It is found that a brane solution in a curved bulk space in Einstein frame corresponds to a dilaton solution in flat space in string frame.

The exact solutions of quantum system with a symmetric well potential V(x) = Dtan²(πx/a) are obtained. The ladder operators are constructed directly from the normalized eigenfunctions with the factorization method. It is shown that these ladder operators satisfy the commutation relations of the generators for an su(1, 1) algebra. The infinitely deep square well and harmonic limits of this potential are briefly studied. The controllability of this system is also investigated. It is demonstrated that this system with discrete bound states can be strongly completely controlled. This may be realized theoretically by acting the creation operator on the ground state.

A class of domain-wall-like solutions of the Skyrme model is obtained analytically. They are described by the tangent hyperbolic function, which is a special limit of the Weierstrass ℘ function. The behavior of one of the two terms in the static energy density is like that of a domain wall. The other term in the static energy density does not vanish but becomes constant at the points far apart from the wall.

In this work, we perform a comparison of the use of distinct gluon propagators with the experimental data in diffractive processes, pp elastic scattering and light meson photo-production. The gluon propagators are calculated through nonperturbative methods, being justified their use in this class of events, due to the smallness of the momentum transfer. Our results are not able to select the best choice for the modified gluon propagator among the analyzed ones. This shows that the application of this procedure in this class of high energy processes, although giving a reasonable fit to the experimental data, should be taken with same caution.

The form of the leptonic mixing matrix emerging from experiment has, in the last few years, generated a lot of interest in the so-called tribimaximal type. This form may be naturally associated with the possibility of a discrete permutation symmetry (S₃) among the three generations. However, trying to implement this attractive symmetry has resulted in some problems and it seems to have fallen out of favor. We suggest an approach in which the S₃ holds to first approximation, somewhat in the manner of the old SU(3) flavor symmetry of the three flavor quark model. It is shown that in the case of the neutrino sector, a presently large experimentally allowed region can be fairly well described in this first approximation. We briefly discuss the nature of the perturbations which are the analogs of the Gell-Mann–Okubo perturbations but confine our attention for the most part to the S₃ invariant model. We postulate that the S₃ invariant mass spectrum consists of nonzero masses for the (τ,b,t) and zero masses for the other charged fermions but approximately degenerate masses for the three neutrinos. The mixing matrices are assumed to be trivial for the charged fermions but of tribimaximal type for the neutrinos in the first approximation. It is shown that this can be implemented by allowing complex entries for the mass matrix and spontaneous breakdown of the S₃ invariance of the Lagrangian.

Based on the ϕ-mapping topological current theory, we show that the presence of the black hole leaves fractional baryon charge outside the horizon in the Einstein–Skyrme theory. A topological current is derived from the Einstein–Skyrme system, which corresponds to the monopoles around the black hole. The branch process (splitting, merging and intersection) is simply discussed during the evolution of the monopoles.

A theory in which four-dimensional space–time is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza–Klein. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U(1) × SU(2) × SU(3) of the standard model. The generalized spin connection in C-space has the properties of Yang–Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb–Ramond fields.

The Hamiltonian formulation of general relativity is considered in finite space–time and a specific reference frame given by the diffeo-invariant components of the Fock simplex in terms of the Dirac–ADM variables.

The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed by the separation of the cosmological scale factor a(x⁰) and its identification with the spatial averaging of the metric determinant, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Nöther theorem. This coincidence allows us to solve the energy constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential perturbations in terms of the Lichnerowicz scale-invariant variables distinguished by the absence of the time derivatives of the spatial metric determinant. It was shown that the Hamiltonian version of the cosmological perturbation theory acquires attributes of the theory of superfluid liquid, and it leads to a generalization of the Schwarzschild solution.

The astrophysical application of this approach to general relativity is considered under supposition that the Dirac–ADM Hamiltonian frame is identified with that of the Cosmic Microwave Background radiation distinguished by its dipole component in the frame of an Earth observer.

The equation of state of deconfined quark matter within the MIT bag model is calculated. This equation of state is used to compute the structure of a neutron star with quark core. It is found that the limiting mass of the neutron star is affected considerably by this modification of the equation of state. Calculations are carried out for different choices of the bag constant.

As a toy model of quantum chromodynamics (QCD), we investigate the influence of the vacuum polarization on the photon propagator, in massless quantum electrodynamics in 2+1 dimensions (QED₃), using the coupled Dyson–Schwinger equations for the fermion and photon propagators with a range of fermion–photon vertices. It is found that the form of the photon propagators in the Nambu–Goldstone and Wigner phases exhibit distinctly different behaviors and it is expected that similar things happen in QCD. Hence in the phenomenological application of QCD one should choose different forms of gluon propagator as input to solve the quark self-energy functions in the two different phases, especially in the study of QCD phase transitions. In addition, employing these results, we discuss the causation of dynamical chiral symmetry breaking (DCSB) in QED₃ and compare it with that in QCD.