Boson Nebulae Charge

We use the first-order approximate solutions to the nonlinear system of Klein-Gordon-Maxwell-Einstein equations describing the minimally coupled charged spin-less field to a spherically symmetric spacetime to analyze a becoming boson star. In the far future and long-range approximation, we derive an analytical time-dependent charge which allows us to point out several significant moments in the evolution of the boson nebula.     

Photo-induced dynamics of Bose-Einstein condensates in optical superlattice

The photo-induced dynamics of cold atoms in a one-dimensional optical superlattice is observed. Steady state distribution of the probability amplitudes and the site population in a one-dimensional optical superlattice is found. It is shown that this solution of the equations, which describes the temporal behavior of a Bose-Einstein condensate in a superlattice, is unstable at the sufficiently high level of boson density. The expression for the increment of modulational instability is obtained on the basis of the linear stability analysis. The numerical examples of non-stationary solutions for boson density in a superlattice for the general model are discussed as applied to both the attraction and repulsion potentials of boson interaction.     

pn-QRPA and higher-order approximations

The proton-neutron Quasi-particle Random Phase Approximation (pn-QRPA) is reviewed and higher-order approximations discussed with reference to the beta decay physics. The approach is fully developed in a boson formalism. Working within a schematic model, we first illustrate a fermion-boson mapping procedure and apply it to construct boson images of the fermion Hamiltonian at different levels of approximation. The quality of these images is tested through a comparison between approximate and exact spectra. Standard QRPA equations are derived in correspondence with the quasi-boson limit of the boson Hamiltonian. The use of higher-order Hamiltonians is seen to improve considerably the stability of the approximate solutions. The mapping procedure is also applied to Fermi beta operators and transition amplitudes are discussed. The range of applicability of the QRPA formalism is examined. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Higgs bosons in the simplest SUSY models

Nowadays, in the MSSM, the moderate values of tan β are almost excluded by the LEP II lower bound on the mass of the lightest Higgs boson. In the next-to-minimal supersymmetric standard model (NMSSM), the theoretical upper bound on it increases and reaches a maximal value in the limit of strong Yukawa coupling, where all solutions to renormalization-group equations are concentrated near the quasifixed point. For a calculation of the Higgs boson spectrum, the perturbation-theory method can be applied. We investigate the particle spectrum within the modified NMSSM, which leads to the self-consistent solution in the limit of strong Yukawa coupling. This model allows one to get m _h～125 GeV at tan β≥1.9. In the model under investigation, the mass of the lightest Higgs boson does not exceed 130.5±3.5 GeV. The upper bound on the mass of the lightest CP-even Higgs boson in more complicated supersymmetric models is also discussed.     

Pair production and vacuum polarization of vector particles with electric dipole moments and anomalous magnetic moments

The matrix 8-component Dirac-like form of the P-odd equations for boson fields of spin 1 and 0 are obtained and the symmetry group of the equations is derived. We found exact solutions of the field equation for vector particles with arbitrary electric and magnetic moments in external constant and uniform electromagnetic fields. The differential probability of pair production of vector particles with electric dipole moments and anomalous magnetic moments by an external constant and uniform electromagnetic field has been found using exact solutions. We have calculated the imaginary and real parts of the electromagnetic field Lagrangian that takes into account the vacuum polarization of vector particles. Received: 14 April 2001 / Revised version: 13 July 2001 / Published online: 19 September 2001     

Derivation and application of the boson method in superconductivity

This is a review article on the boson method in superconductivity. It covers derivations of the basic equations in the boson method and applications of these equations to the magnetic properties of type II superconductors and to the Josephson phenomena.     

Grand unification of effective gauge theories

An effective non-renormalizable SU(3)×SU(2)×U(1) invariant gauge theory results at ordinary energies when superheavy fields are integrated out from a grand unified theory based on a simple gauge group G. The solutions of the second-order renormalization-group equations for the gauge coupling constants of the effective theory are examined. General formulae for the superheavy vector boson mass and for sin²θ near M_W are given in this approach to grand unification. The superheavy vector boson mass is plotted against the QCD scale parameter Λ for a certain set of grand unified models. Corrections to the prediction when the set of models is enlarged are discussed, and illustrated with examples from G≡SU(5) and O(10).     

Relativistic wave equation for a boson-fermion system

We present a two-body relativistic wave equation for a system composed of a boson and a fermion. One-body equations such as the Dirac and the Klein-Gordon equations are often used as an approximate equation for relativistic two-body systems. However, when the masses of two particles are not very different, the use of one-body equations comes into question. We use the Feshbach-Villars formalism for the boson so that the wave equation can be given in the form of an eigenvalue equation for the Hamiltonian. Differences between our equation and the one-body equations are examined and illustrated in a numerical example of a two-body system with scalar and vector potentials.Communicated by: W. Weise     

A Rigorous Formulation of the Boson Method in Superconductivity

A rigorous formulation of the boson method in superconductivity is presented. Assuming the local gauge invariance and presence of a phase-dependent order parameter and utilizing the path-integral formalism, we derive a set of macroscopic equations which control all the superconducting states. These equations are model-independent. They contain certain functions and parameters which should be calculated for a given model. Using this rigorous formulation, we study what kind of approximations are involved in the usual formulation of the boson method and how these approximations can be improved.     

General Relativistic Bound States of a Fermion and a Scalar Interacting via a Massive Scalar

A complete set of numerical solutions is obtained, in the ladder approximation, to the Bethe-Salpeter equation describing bound states of a spin- fermion and spin-0 boson with arbitrary masses that interact via the exchange of a massive, spin-0 boson. The equation has been used previously, without solutions actually being calculated, to derive some properties of nucleons by treating the physical nucleon as a bound state of a “bare” nucleon and a “bare” meson. It is likely that most, if not all, two-body, bound-state Bethe-Salpeter equations can be solved in the ladder approximation using the method discussed here.     

Boson expansions and quantization of time-dependent self-consistent fields (I). Particle-hole excitations

Two concrete methods are presented for quantizing the time-dependent Hartree equations in terms of boson operators. The first is the well-known infinite boson expansion analogous to the Holstein-Primakoff representation of angular momentum operators. The second, a new development, consists of finite boson quadratic forms, and is analogous to the Schwinger representation of angular momenta. In each case, a physical boson subspace can easily be constructed within which the full fermion dynamics is exactly duplicated. It therefore follows that quantization of the time-dependent Hartree equations, including all degrees of freedom, retrieves the exact many-body problem. The discussion in this paper is limited to particle-hole excitations of an N-particle system. A generalization to one-nucleon transfer processes on the N-particle system is also given in terms of ideal odd nucleons, but this brings in infinite expansions.     

The Importance of Boundary Conditions in Solving the Bound-State Bethe-Salpeter Equation

The characteristic of bound-state, Bethe-Salpeter equations that makes them so difficult to solve numerically can be overcome, in some if not many cases, by expanding solutions in terms of basis functions that obey the boundary conditions that are satisfied by the solutions. The utility of such basis functions is demonstrated by calculating the zero-energy, bound-state solutions of a spin-0 boson and a spin-&frac; fermion with unequal masses. The constituents interact via scalar electrodynamics and are described by the Bethe-Salpeter equation in the ladder approximation. Although the Bethe-Salpeter equation that is solved is separable in the zero-energy limit, the feature that typically prevents solutions from being obtained numerically is still present. A technique for calculating boundary conditions, which is readily generalized to other Bethe-Salpeter equations, is discussed in detail.Supported by a grant from the Ohio Supercomputer CenterReceived January 31, 2003; accepted April 4, 2003 Published online August 25, 2003     

The quantum Fokker-Planck equation for certain boson systems

Quantum relations between a class of boson Langevin equations and the associated Fokker-Planck equations are derived. The Fokker-Planck equations for the Wigner distribution Φ_sym related with symmetric ordering of the boson operators, the distribution Φ_A related with antinormal ordering, and the distribution Φ_N related with normal ordering (P-representation) are given.     

Particle spectrum in the modified nonminimal supersymmetric standard model in the strong Yukawa coupling regime

A theoretical analysis of solutions of renormalization group equations in the minimal supersymmetric standard model, which lead to a quasi-fixed point has shown that the mass of the lightest Higgs boson in these models does not exceed 94 ± 5 GeV. This implies that a considerable part of the parameter space in the minimal supersymmetric model is in fact eliminated by existing LEPII experimental data. In the nonminimal supersymmetric standard model the upper bound on the mass of the lightest Higgs boson reaches its maximum in the strong Yukawa coupling regime when the Yukawa constants are substantially greater than the gauge constants on the grand unification scale. In the present paper the particle spectrum is studied using the simplest modification of the nonminimal supersymmetric standard model which gives a self-consistent solution in this region of parameter space. This model can give m _h ～ 125 GeV even for comparatively low values of β ≥ 1.9. The spectrum of Higgs bosons and neutralinos is analyzed using the method of diagonalizing mass matrices proposed earlier. In this model the mass of the lightest Higgs boson does not exceed 130.5 ± 3.5 GeV.     

Compact boson stars

We consider compact boson stars that arise for a V-shaped scalar field potential. They represent a one parameter family of solutions of the scaled Einstein–signum–Gordon equations. We analyze the physical properties of these solutions and determine their domain of existence. Along their physically relevant branch emerging from the compact Q-ball solution, their mass increases with increasing radius. Employing arguments from catastrophe theory we argue that this branch is stable, until the maximal value of the mass is reached. There the mass and size are on the order of magnitude of the Schwarzschild limit, and thus the spiraling respectively oscillating behaviour, well known for compact stars, sets in.     

Modified Scattering for the Boson Star Equation

We consider the question of scattering for the boson star equation in three space dimensions. This is a semi-relativistic Klein-Gordon equation with a cubic nonlinearity of Hartree type. We combine weighted estimates, obtained by exploiting a special null structure present in the equation, and a refined asymptotic analysis performed in Fourier space, to obtain global solutions evolving from small and localized Cauchy data. We describe the behavior of such solutions at infinity by identifying a suitable nonlinear asymptotic correction to scattering. As a byproduct of the weighted energy estimates alone, we also obtain global existence and (linear) scattering for solutions of semi-relativistic Hartree equations with potentials decaying faster than Coulomb.     

A possibility of asymptotic freedom without non-Abelian gauge theories

We discuss solutions of the renormalization group equations for a Yukawa field theory. For an increasing effective boson mass we find that the leading terms in the vertex functions in the high-energy region are given by diagrams which contain no internal boson lines. In e⁺e^? annihilation into hadrons we get the parton model formula R(s) = Σ_iQ_i², whereas in the deep inelastic e^?p scattering the simple parton model behaviour is modified by the (in general) non-canonical dimension of the quark field.     

Spatially compact solutions and stabilization in Einstein-Yang-Mills-Higgs theories

New solutions to the static, spherically symmetric Einstein-Yang-Mills-Higgs equations with the Higgs field in the triplet (doublet) representation are presented. They form continuous families parametrized by alpha = M(W)/M(Pl) [M(W) (M(Pl)) denoting the W boson (the Planck) mass]. The corresponding space-times are regular and have spatially compact sections. A particularly interesting class with the Yang-Mills amplitude being nodeless is exhibited and is shown to be linearly stable with respect to spherically symmetric perturbations. For some solutions with nodes of the Yang-Mills amplitude a new stabilization phenomenon is found, according to which their unstable modes disappear as alpha increases (for the triplet) or decreases (for the doublet).     

Quantum melting and absence of Bose-Einstein condensation in two-dimensional vortex matter

We demonstrate that quantum fluctuations suppress Bose-Einstein condensation of quasi-two-dimensional bosons in a rapidly rotating trap. Our conclusions rest in part on the derivation of an exact expression for the boson action in terms of vortex position coordinates, and in part on a solution of the weakly interacting boson Bogoliubov equations, which simplify in the rapid-rotation limit. We obtain analytic expressions for the collective-excitation dispersion, which is quadratic rather than linear. Our estimates for the boson filling factor at which the vortex lattice melts are consistent with recent exact-diagonalization calculations.     

Studies of the classical energy limit of the interacting boson model in the case of three-body interactions

In this study of the classical energy limit of an interacting boson model with three-body interactions, two variants are considered: the inclusion of cubic d-boson interaction terms and the inclusion of three-body O(6) symmetric quadrupole operator terms. The solutions of the corresponding energy minimum condition equations are used for analysis of the triaxiality of the nuclear shape in the first case and for analysis of spherical—prolate—oblate shape phase transitions in the second case. The text was submitted by the authors in English.