1,060 research outputs found
Highest coefficient of scalar products in SU(3)-invariant integrable models
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe
ansatz. Scalar products of Bethe vectors in such models can be expressed in
terms of a bilinear combination of their highest coefficients. We obtain
various different representations for the highest coefficient in terms of sums
over partitions. We also obtain multiple integral representations for the
highest coefficient.Comment: 17 page
Fractional Generalization of Gradient Systems
We consider a fractional generalization of gradient systems. We use
differential forms and exterior derivatives of fractional orders. Examples of
fractional gradient systems are considered. We describe the stationary states
of these systems.Comment: 11 pages, LaTe
A Complete Version of the Glauber Theory for Elementary Atom - Target Atom Scattering and Its Approximations
A general formalism of the Glauber theory for elementary atom (EA) - target
atom (TA) scattering is developed. A second-order approximation of its complete
version is considered in the framework of the optical-model perturbative
approach. A `potential' approximation of a second-order optical model is
formulated neglecting the excitation effects of the TA. Its accuracy is
evaluated within the second-order approximation for the complete version of the
Glauber EA-TA scattering theory.Comment: PDFLaTeX, 10 pages, no figures; an updated versio
Polytropic configurations with non-zero cosmological constant
We solve the equation of the equilibrium of the gravitating body, with a
polytropic equation of state of the matter , with
, in the frame of the Newtonian gravity, with non-zero
cosmological constant . We consider the cases with
and construct series of solutions with a fixed value of . For each
value of , the non-dimensional equation of the static equilibrium has a
family of solutions, instead of the unique solution of the Lane-Emden equation
at . The equilibrium state exists only for central densities
larger than the critical value . There are no static solutions
at . We find the values of for each value of and
show that the presence of dark energy decrease the dynamic stability of the
configuration. We apply our results for analyzing the possibility of existence
of equilibrium states for cluster of galaxies in the present universe with
non-zero .Comment: submitted to Astron. A
Mickelsson algebras and Zhelobenko operators
We construct a family of automorphisms of Mickelsson algebra, satisfying
braid group relations. The construction uses 'Zhelobenko cocycle' and includes
the dynamical Weyl group action as a particular case
Quantum properties of a non-Abelian gauge invariant action with a mass parameter
We continue the study of a local, gauge invariant Yang-Mills action
containing a mass parameter, which we constructed in a previous paper starting
from the nonlocal gauge invariant mass dimension two operator F_{\mu\nu}
(D^2)^{-1} F_{\mu\nu}. We return briefly to the renormalizability of the model,
which can be proven to all orders of perturbation theory by embedding it in a
more general model with a larger symmetry content. We point out the existence
of a nilpotent BRST symmetry. Although our action contains extra
(anti)commuting tensor fields and coupling constants, we prove that our model
in the limit of vanishing mass is equivalent with ordinary massless Yang-Mills
theories. The full theory is renormalized explicitly at two loops in the MSbar
scheme and all the renormalization group functions are presented. We end with
some comments on the potential relevance of this gauge model for the issue of a
dynamical gluon mass generation.Comment: 17 pages. v2: version accepted for publication in Phys.Rev.
- âŠ