Stable Fermion Bag Solitons in the Massive Gross-Neveu Model: Inverse Scattering Analysis

Formation of fermion bag solitons is an important paradigm in the theory of hadron structure. We study this phenomenon non-perturbatively in the 1+1 dimensional Massive Gross-Neveu model, in the large $N$ limit. We find, applying inverse scattering techniques, that the extremal static bag configurations are reflectionless, as in the massless Gross-Neveu model. This adds to existing results of variational calculations, which used reflectionless bag profiles as trial configurations. Only reflectionless trial configurations which support a single pair of charge-conjugate bound states of the associated Dirac equation were used in those calculations, whereas the results in the present paper hold for bag configurations which support an arbitrary number of such pairs. We compute the masses of these multi-bound state solitons, and prove that only bag configurations which bear a single pair of bound states are stable. Each one of these configurations gives rise to an O(2N) antisymmetric tensor multiplet of soliton states, as in the massless Gross-Neveu model.Comment: 10 pages, revtex, no figures; v2: typos corrected, references added; v3: version accepted for publication in the PRD. referencess added. Some minor clarifications added at the beginning of section

Duality and Representations for New Exotic Bialgebras

We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic bialgebras S03 and S14 which are not deformations of the of the classical algebras of functions on GL(2) or GL(1|1). With this we finalize the classification of the matrix bialgebras which unital associative algebras generated by four elements. We also find the corresponding dual bialgebras of these new exotic bialgebras and study their representation theory in detail. We also discuss in detail a special case of R_{S1,4} in which the corresponding algebra turns out to be a special case of the two-parameter quantum group deformation GL_{p,q}(2).Comment: 33 pages, LaTeX2e, using packages: cite,amsfonts,amsmath,subeqn; reference updated; v3: corrections in subsection 3.

Partial waves of baryon-antibaryon in three-body B meson decay

The conspicuous threshold enhancement has been observed in the baryon-antibaryon subchannels of many three-body B decay modes. By examining the partial waves of baryon-antibaryon, we first show for B- -->pp-bar K- that the pK- angular correlation rules out dominance of a single pp-bar partial wave for the enhancement, for instance, the resonance hypothesis or the strong final-state interaction in a single channel. The measured pK- angular correlation turns out to be opposite to the naive expectation of the short-distance picture. We study the origin of this reversed angular correlation in the context of the pp-bar partial waves and argue that NN-bar bound states may be the cause of this sign reversal. Dependence of the angular correlation on the pp-bar invariant mass is very important to probe the underlying problem from the experimental side.Comment: 16 pages, 9 figures, the version for journal publicatio

Algebraic Framework for Quantization of Nonultralocal Models

Extension of the braid relations to the multiple braided tensor product of algebras that can be used for quantization of nonultralocal models is presented. The Yang--Baxter--type consistency conditions as well as conditions for the existence of the multiple coproduct (monodromy matrix), which can be used for construction of the commuting subalgebra, are given. Homogeneous and local algebras are introduced, and simplification of the Yang--Baxter--type conditions for them is shown. The Yang--Baxter--type equations and multiple coproduct conditions for homogeneous and local of order 2 algebras are solved.Comment: 18 pages, Latex, one formula plus two citations added, several misprints were correcte

Hom-quantum groups I: quasi-triangular Hom-bialgebras

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi-triangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel'd's quantum enveloping algebras. Each quasi-triangular Hom-bialgebra comes with a solution of the quantum Hom-Yang-Baxter equation, which is a non-associative version of the quantum Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained from modules of suitable quasi-triangular Hom-bialgebras.Comment: 21 page

Parity violation in low energy neutron deuteron scattering

Parity violating effects for low energy elastic neutron deuteron scattering are calculated for DDH and EFT-type of weak potentials in a Distorted Wave Born Approximation, using realistic hadronic strong interaction wave functions, obtained by solving three-body Faddeev equations in configuration space. The results of relation between physical observables and low energy constants can be used to fix low energy constants from experiments. Potential model dependencies of parity violating effects are discussed.Comment: version accepted for publication in Phys. Rev.

On the exactly solvable pairing models for bosons

We propose the new exactly solvable model for bosons corresponding to the attractive pairing interaction. Using the electrostatic analogy, the solution of this model in thermodynamic limit is found. The transition from the superfluid phase with the Bose condensate and the Bogoliubov - type spectrum of excitations in the weak coupling regime to the incompressible phase with the gap in the excitation spectrum in the strong coupling regime is observed.Comment: 19 page

On string solutions of Bethe equations in N=4 supersymmetric Yang-Mills theory

The Bethe equations, arising in description of the spectrum of the dilatation operator for the su(2) sector of the N=4 supersymmetric Yang-Mills theory, are considered in the anti-ferromagnetic regime. These equations are deformation of those for the Heisenberg XXX magnet. It is proven that in the thermodynamic limit roots of the deformed equations group into strings. It is proven that the corresponding Yang's action is convex, which implies uniqueness of solution for centers of the strings. The state formed of strings of length (2n+1) is considered and the density of their distribution is found. It is shown that the energy of such a state decreases as n grows. It is observed that non-analyticity of the left hand side of the Bethe equations leads to an additional contribution to the density and energy of strings of even length. Whence it is concluded that the structure of the anti-ferromagnetic vacuum is determined by the behaviour of exponential corrections to string solutions in the thermodynamic limit and possibly involves strings of length 2.Comment: LaTex, 9 pages, 1 figur

Remarks on the Reduced Phase Space of (2+1)-Dimensional Gravity on a Torus in the Ashtekar Formulation

We examine the reduced phase space of the Barbero-Varadarajan solutions of the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We show that it is a finite-dimensional space due to existence of an infinite dimensional residual gauge invariance which reduces the infinite-dimensional space of solutions to a finite-dimensional space of gauge-inequivalent solutions. This is in agreement with general arguments which imply that the number of physical degrees of freedom for (2+1)-dimensional Ashtekar gravity on a torus is finite.Comment: 13 pages, Latex. More details have been included and the expression for the finite residual gauge transformations has been worked ou

Dynamical mapping method in nonrelativistic models of quantum field theory

The solutions of Heisenberg equations and two-particles eigenvalue problems for nonrelativistic models of current-current fermion interaction and $N, \Theta$ model are obtained in the frameworks of dynamical mapping method. The equivalence of different types of dynamical mapping is shown. The connection between renormalization procedure and theory of selfadjoint extensions is elucidated.Comment: 14 page