Related papers: New spin generalisation for long range interaction…
An algebra ${\cal G}$ of symmetric {\em one-particle} operators is constructed for the Calogero model. This is an infinite-dimensional Lie-algebra, which is independent of the interaction parameter $\lambda$ of the model. It is constructed…
A short survey is presented on spin--glass--like states characteristics in complex nonmagnetic systems. We discuss the interplay of the interaction structure and symmetry with the classification scenarios of the replica symmetry breaking.…
We introduce and analyze an extended Hubbard model, in which intersite Coulomb interaction as well as a staggered local potential (SLP) are considered, on the square lattice at half band filling, in the thermodynamic limit. Using both…
In these lectures, I review some recent results on the Calogero-Sutherland model and the Haldane Shastry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonian and fractional statistics. The form factor…
Using an elaborate set of simulational tools and statistically optimized methods of data analysis we investigate the scaling behavior of the correlation lengths of three-dimensional classical O($n$) spin models. Considering…
We show that, in any conformal field theory, the weights of all bulk primary fields that couple to N phi_{2,1} fields on the boundary are given by the spectrum of an N-particle Calogero-Sutherland model. The corresponding correlation…
The Calogero model with external harmonic oscillator potential is discussed from sL(2,R) algebra point of view. Explicit formulae for functions with exponential time behaviour are given; in particular, the integrals of motion are…
We show that the Calogero and Calogero-Sutherland models possess an N-body generalization of shape invariance. We obtain the operator representation that gives rise to this result, and discuss the implications of this result, including the…
We consider a three-dimensional lattice Abelian Higgs gauge model for a charged $N$-component scalar field ${\phi}$, which is invariant under $SO(N)$ global transformations for generic values of the parameters. We focus on the…
For a one-dimensional model in which the two-body interactions are long-range and strong, the system almost crystallizes. The harmonic modes of such a lattice can be used to compute the ground state wave function and the dynamical…
We construct a class of interacting spin Calogero-Moser type systems. They can be regarded as a many particle system with spin degrees of freedom and as an integrable spin chain of Gaudin type. We prove that these Hamiltonian systems are…
We discuss various examples of classical Calogero-Moser models with internal degrees of freedom. These models besides of having some attractive properties, like the complete integrability, are of interest eg., in studying spectral…
Higher spin fields in four dimensions, and more generally conformal fields in arbitrary dimensions, can be described by spinning particle models with a gauged SO(N) extended supergravity on the worldline. We consider here the one-loop…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings need not be unified at the GUT scale due to the high-dimensional operators. Considering gravity mediated supersymmetry breaking, we study for the first time the…
We present a generalization of the non-Abelian version of the $CP^{N-1}$ models (also known as Grassmannian models) that involve composite gauge fields to accommodate partial breaking of the non-Abelian gauge symmetry. For this to be…
We review some recent results on the Calogero-Sutherland model with emphasis upon its algebraic aspects. We give integral formulae for excited states (Jack polynomials) of this model and their relations with W_n singular vectors and…
The energy-momentum and spin tensors for a given theory can be replaced by alternative expressions that obey the same conservation laws for the energy, linear momentum, as well as angular momentum but, however, differ by the local…
We present a detailed analysis of the spin models with near-neighbors interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214] by a suitable generalization of the exchange operator formalism. We provide a complete…
We explore a class of CFT's with higher spin currents and charges. Away from the free or $N=\infty$ limit the non-conservation of currents is governed by operators built out of the currents themselves, which deforms the algebra of charges…