Related papers: Generalized Calogero model in arbitrary dimensions
Motivated by recently explored examples, we undertake a systematic study of conformal invariance in one-dimensional sigma models where an isometry group has been gauged. Perhaps surprisingly, we uncover classes of sigma models which are…
We discuss the structure of 2D conformal field theories (CFT) at central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b…
We adopt a geometric perspective on Fock space to provide two complementary insights into the eigenstates in many-body-localized fermionic systems. On the one hand, individual many-bodylocalized eigenstates are well approximated by a Slater…
This is a continuation of the preceding paper (hep-ph/0108219). First of all we make a brief review of generalized coherent states based on Lie algebra su(1,1) and prove that the resolution of unity can be obtained by the curvature form of…
Conformal blocks for correlation functions of tensor operators play an increasingly important role for the conformal bootstrap programme. We develop a universal approach to such spinning blocks through the harmonic analysis of certain…
A new approach to obtaining open Universes models as exact solutions of gravitational equations is considered. The proposed method is based on an analogy between electrostatics of conductors and open cosmological models which have a…
We argue that fermion-boson mapping techniques represent a natural tool for studying many-body supersymmetry in fermionic systems with pairing. In particular, using the generalized Dyson mapping of a many-level fermion superalgebra with the…
We study new interactions between degrees of freedom for Calogero, Sutherland and confined Calogero spin models. These interactions are encoded by the generators of the Lie algebra so(N) or sp(N). We find the symmetry algebras of these new…
We extend various recent results regarding the derivation of effective cosmological Friedmann equations from the dynamics of group field theory (GFT). Restricting ourselves to a single GFT field mode (or fixed values of Peter-Weyl…
We apply the nonlinear realizations method for constructing new Galilean conformal mechanics models. Our starting point is the Galilean conformal algebra which is a non-relativistic contraction of its relativistic counterpart. We calculate…
Calogero-Sutherland models of $N$ identical particles on a circle are deformed away from hermiticity but retaining a $\cal PT$ symmetry. The interaction potential gets completely regularized, which adds to the energy spectrum an infinite…
Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…
This paper concerns the construction of $su(r+1)$ Barut--Girardello coherent states in term of generalized Grassmann variables. We first introduce a generalized Weyl-Heisenberg algebra ${\cal A}(r)$ ($r \geq 1$) generated by $r$ pairs of…
A model describing N particles on a line interacting pairwise via an elliptic function potential in the presence of an external field is partially solved in the quantum case in a totally algebraic way. As an example, the ground state and…
Analytic-bilinear approach is used to study continuous and discrete non-isospectral symmetries of the generalized KP hierarchy. It is shown that M\"obius symmetry transformation for the singular manifold equation leads to continuous or…
The reductions of the free geodesic motion on a non-compact simple Lie group G based on the $G_+ \times G_+$ symmetry given by left- and right multiplications for a maximal compact subgroup $G_+ \subset G$ are investigated. At generic…
For massive and conformal quantum field theories in 1+1 dimensions with a global gauge group we consider soliton automorphisms, viz. automorphisms of the quasilocal algebra which act like two different global symmetry transformations on the…
We construct certain eigenfunctions of the Calogero-Sutherland hamiltonian for particles on a circle, with mixed boundary conditions. That is, the behavior of the eigenfunction, as neighbouring particles collide, depend on the pair of…
The Schr\"odinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have…
We construct several new families of exactly and quasi-exactly solvable BC_N-type Calogero-Sutherland models with internal degrees of freedom. Our approach is based on the introduction of two new families of Dunkl operators of B_N type…