379 research outputs found
SU(5) Gravitating Monopoles
Spherically symmetric solutions of the SU(5) Einstein-Yang-Mills-Higgs system
are constructed using the harmonic map ansatz \cite{IS}. This way the problem
reduces to solving a set of ordinary differential equations for the appropriate
profile functions.Comment: 12 pages, 3 Figure
Quadratic integrals of motions for the systems of identical particles-quantum case
The quantum dynamical systems of identical particles admitting an additional
integral quadratic in momenta are considered. It is found that an appropriate
ordering procedure exists which allows to convert the classical integrals into
their quantum counterparts. The relation to the separation of variables in
Schroedinger equation is discussed.Comment: 6 pages, no figure
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 Scrh\"odinger equations. Some relativistic counterparts of these
problems are also discussed.Comment: 8 pages, latex, no figure
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.Comment: RevTeX, 6 pages, 8 figure
On Spherically-Symmetric Solutions in the Two-Higgs Standard Model
We report the results of a numerical search for non-topological solitons in
the two-Higgs standard model, characterized by the non-trivial winding,
, of the relative phase of the two doublets. In a region of
(weak-coupling) parameter space we identify a branch of winding solutions,
which are lower in energy than the embedded standard sphaleron and deformed
(bi)sphalerons. Contrary, however, to what happens in 2d toy models, these
solutions remain unstable even for very large Higgs masses.Comment: 11 LaTeX pages including 3 .eps figure
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.Comment: 38 pages, late
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