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Y. Brihaye

Publications and source records attributed to Y. Brihaye.

At least 91 records · Page 5Linked to original sources
arXiv2001

Classical solutions in the Einstein-Born-Infeld-Abelian-Higgs model

We consider the classical equations of the Born-Infeld-Abelian-Higgs model (with and without coupling to gravity) in an axially symmetric ansatz. A numerical analysis of the equations reveals that the (gravitating) Nielsen-Olesen vortices are smoothly deformed by the Born-Infeld interaction, characterized by a coupling constant $β^2$, and that these solutions cease to exist at a critical value of $β^2$. When the critical value is approached, the length of the magnetic field on the symmetry axis becomes infinite.

hep-th↗
arXiv2000

Quasi exactly solvable matrix Schroedinger operators

Two families of quasi exactly solvable 2*2 matrix Schroedinger operators are constructed. The first one is based on a polynomial matrix potential and depends on three parameters. The second is a one-parameter generalisation of the scalar Lame equation. The relationship between these operators and QES Hamiltonians already considered in the literature is pointed out.

quant-ph↗
arXiv2000

Finite energy/action solutions of $p_1$ Yang-Mills equations on $p_2$ Schwarzschild and deSitter backgrounds for dimension $d \ge 4$

Physically relevant gauge and gravitational theories can be seen as special members of hierarchies of more elaborate systems. The Yang-Mills (YM) system is the first member of a hierarchy of Lagrangians which we will index by $p_1$, and the Einstein-Hilbert (EH) system of general relativity is the first member of another hierarchy which we index by $p_2$. In this paper, we study the classical equations of the $p_1 = 1,2$ YM hierarchy considered in the background of special geometries (Schwarzschild, deSitter,anti-deSitter) of the $p_2=1,2,3$ EH hierarchy. Solutions are obtained in various dimensions and lead to several examples of non-self-dual YM fields. When $p_1=p_2$ self-dual solutions exist in addition. Their action is equal to the Chern-Pontryagin charge and can be compared with that of the non-self-dual solutions.

hep-th↗
arXiv2000

Classical solutions of the Gravitating Abelian Higgs Model

We consider the classical equations of the gravitating Abelian-Higgs model in an axially symmetric ansatz. More properties of the solutions of these equations (the Melvin and the sting branches) are presented. These solutions are also constructed for winding numbers N=2. It is shown that these vortices exist in attractive and repulsive phases, separated by the value of the Higgs coupling constant parameter leading to self-dual equations.

hep-th↗
arXiv2000

Gravitating monopole and black holes at intermediate Higgs masses

Self-gravitating SU(2) Higgs magnetic monopoles exist up to a critical value of the ratio of the vector meson mass to the Planck mass, which depends on the Higgs boson mass. At the critical value a critical solution with a degenerate horizon is reached. As pointed out by Lue and Weinberg, there are two types of critical solutions, with a transition at an intermediate Higgs boson mass. Here we investigate this transition for black holes, and reconsider it for the case of gravitating monopoles.

hep-th↗
arXiv2000

Gravitating (bi-)sphalerons

The standard model of electroweak interactions is minimally coupled to gravity and the response of the spherically symmetric solutions -the sphaleron and the bisphaleron- to gravity is emphasized. For a given value of the Higgs mass $M_H$, several branches of solutions exist which terminate into cusp-catastrophy at some ($M_H$-depending) critical value of the parameter $α$ defined by the ratio of the vector-boson mass to the Planck mass. A given branch either bifurcates from another one at an intermediate value of $α$ or persists in the limit $α\to 0$ where it terminates into a flat sphaleron or bisphaleron or into a Bartnik-McKinnon solution. These bifurcation patterns are studied in some details.

hep-th↗
arXiv1999

Gravitating dyons and the Lue-Weinberg bifurcation

Gravitating t'Hooft-Polyakov magnetic monopoles can be constructed when coupling the Georgi-Glashow model to gravitation. For a given value of the Higgs boson mass, these gravitating solitons exist up to a critical value of the ratio of the vector meson mass to the Planck mass. The critical solution is characterized by a degenerate horizon of the metric. As pointed out recently by Lue and Weinberg, two types of critical solutions can occur, depending on the value of the Higgs boson mass. Here we investigate this transition for dyons and show that the Lue and Weinberg phenomenon is favorized by the presence of the electric-charge degree of freedom.

hep-th↗
arXiv1999

Dyonic Non-Abelian Black Holes

We study static spherically symmetric dyonic black holes in Einstein-Yang-Mills-Higgs theory. As for the magnetic non-abelian black holes, the domain of existence of the dyonic non-abelian black holes is limited with respect to the horizon radius and the dimensionless coupling constant $α$, which is proportional to the ratio of vector meson mass and Planck mass. At a certain critical value of this coupling constant, $\hat α$, the maximal horizon radius is attained. We derive analytically a relation between $\hat α$ and the charge of the black hole solutions and confirm this relation numerically. Besides the fundamental dyonic non-abelian black holes, we study radially excited dyonic non-abelian black holes and globally regular gravitating dyons.

hep-th↗
arXiv1998

On realizations of nonlinear Lie algebras by differential operators

We study realizations of polynomial deformations of the sl(2,R)- Lie algebra in terms of differential operators strongly related to bosonic operators. We also distinguish their finite- and infinite-dimensional representations. The linear, quadratic and cubic cases are explicitly visited but the method works for arbitrary degrees in the polynomial functions. Multi-boson Hamiltonians are studied in the context of these ``nonlinear'' Lie algebras and some examples dealing with quantum optics are pointed out.

hep-th↗
arXiv1998

The Goldstone model static solutions on S^1

We study in a systematic way all static solutions of the Goldstone model in 1+1 dimension with a periodicity condition on the spatial coordinate. The solutions are presented in terms of the standard trigonometric functions and of Jacobi elliptic functions. Their stability analysis is carried out, and the complete list of classical stable quasi-topological solitons is given.

hep-th↗
arXiv1998

Dyon-Skyrmion Lumps

We make a numerical study of the classical solutions of the combined system consisting of the Georgi-Glashow model and the SO(3) gauged Skyrme model. Both monopole-Skyrmion and dyon-Skyrmion solutions are found. A new bifurcation is shown to occur in the gauged Skyrmion solution sector.

hep-th↗
arXiv1996

Irreducible Representations of an Algebra underlying Hidden Symmetries of a class of Quasi Exactly Solvable Systems of Equations

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional representations of this algebra are classified into five infinite discrete sets and one exceptional case. Their matrix elements are given explicitely. The results are related to the theory of quasi exactly solvable equations.

solv-int↗
arXiv1995

Galilean invariance in 2+1 dimensions

The Galilean invariance in three dimensional space-time is considered. It appears that the Galilei group in 2+1 dimensions posses a three-parameter family of projective representations. Their physical interpretation is discussed in some detail.

hep-th↗
arXiv1995

Central potential and examples of hidden algebra structure

We propose two generalisations of the Coulomb potential equation of quantum mechanics and investigate the occurence of algebraic eigenfunctions for the corresponding Scrhödinger equations. Some relativistic counterparts of these problems are also discussed.

hep-th↗
arXiv1994

Projectivised representations of $U_q osp(2,2)$

We construct representations of the enveloping algebra $U_q osp(2,2)$ in terms of finite difference operators and we discuss this result in the framework of quasi-exactly-solvable equations.

hep-th↗