Exchange Operator Formalism for Integrable Systems of Particles

Abstract

We formulate one dimensional many-body integrable systems in terms of a new set of phase space variables involving exchange operators. The hamiltonian in these variables assumes a decoupled form. This greatly simplifies the derivation of the conserved charges and the proof of their commutativity at the quantum level.

8 pages

Cited by in corpus (244)

• Supersymmetry and Quantum Mechanics
• Yang-Baxter equation in spin chains with long range interactions
• Exact operator solution of the Calogero-Sutherland model
• Physics and Mathematics of Calogero particles
• Explicit Solution to the N-Body Calogero Problem
• Lattice Integrable Systems of Haldane-Shastry Type
• Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics
• Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics
• An infinite family of solvable and integrable quantum systems on a plane
• Relativistic Calogero-Moser model as gauged WZW theory
• Fractional Statistics in One-Dimension: View From An Exactly Solvable Model
• Integrable Systems for Particles with Internal Degrees of Freedom
• The Calogero Model - Anyonic Representation, Fermionic Extension and Supersymmetry
• Deformed Heisenberg algebra with reflection
• Solution of Some Integrable One-Dimensional Quantum Systems
• Spectrum of a spin chain with inverse square exchange
• The Sine-Gordon Solitons as a N-Body Problem
• Harmonic oscillator with minimal length uncertainty relations and ladder operators
• Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators
• On Domain-Wall/QFT Dualities in Various Dimensions
• Spinons in Conformal Field Theory
• Invariants of the Haldane-Shastry $SU(N)$ Chain
• Quantum Calogero-Moser Models: Integrability for all Root Systems
• Common Algebraic Structure for the Calogero-Sutherland Models
• The Calogero-Sutherland Model and Polynomials with Prescribed Symmetry
• Quantum vs Classical Integrability in Calogero-Moser Systems
• Global properties of the spectrum of the Haldane-Shastry spin chain
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• $C_{\lambda }$-extended harmonic oscillator and (para)supersymmetric quantum mechanics
• The R-matrix structure of the Euler-Calogero-Moser model
• Hidden nonlinear supersymmetries in pure parabosonic systems
• Inequivalent Quantizations of the Rational Calogero Model
• Approach to a Parity Deformed Jaynes-Cummings Model and the Maximally Entangled States
• Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd $k$
• Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
• Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model
• Exact Solution of the Sutherland Model with arbitrary symmetry
• Haldane-Shastry spin chains of BC_N type
• Supersymmetry, Shape Invariance and Solvability of $A_{N-1}$ and $B{C}_N$ Calogero-Sutherland Model
• Three aspects of bosonized supersymmetry and linear differential field equation with reflection
• From Coxeter Higher-Spin Theories to Strings and Tensor Models
• A_N-type Dunkl operators and new spin Calogero-Sutherland models
• New Family of Solvable 1D Heisenberg Models
• On Dunkl angular momenta algebra
• Quantum Quench of the trap frequency in the harmonic Calogero model
• Integrable $1/r^2$ Spin Chain with Reflecting End
• The quantum angular Calogero-Moser model
• Bound States in One-Dimensional Quantum N-Body Systems with Inverse Square Interaction
• The algebra of q-pseudodifferential symbols and the q-W_{KP}^n algebra
• Periodic integrable systems with delta-potentials
• Integrals of motion of the Haldane Shastry Model
• Dunkl-Graphene in constant magnetic field
• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• New spin Calogero-Sutherland models related to B_N-type Dunkl operators
• Bosonization of current-current interactions
• Nonlinear supersymmetry in the quantum Calogero model
• Super-Calogero-Moser-Sutherland systems and free super-oscillators : a mapping
• Local exclusion and Lieb-Thirring inequalities for intermediate and fractional statistics
• Supersymmetric Quantum Mechanics with Reflections
• Integer Partitions and Exclusion Statistics
• On the equivalence of the rational Calogero-Moser system to free particles
• Two-Dimensional Unoriented Strings And Matrix Models
• Novel correlations in two dimensions: Some exact solutions
• Yangian Symmetry and Quantum Inverse Scattering Method for the One-Dimensional Hubbard Model
• Cat-States in the Framework of Wigner-Heisenberg Algebra
• Spin-Charge Separation at Finite Temperature in the Supersymmetric t-J Model with Long-Range Interactions
• Hidden algebra of the $N$-body Calogero problem
• Shape Invariance in the Calogero and Calogero-Sutherland Models
• A Note on Dressed S-Matrices in Models with Long-Range Interactions
• Orthogonal Symmetric Polynomials Associated with the Calogero Model
• A note on the eigenvectors of long-range spin chains and their scalar products
• A multispecies Calogero model
• A multispecies Calogero-Sutherland model
• Bosonic realization of algebras in the Calogero model
• Exact Dynamical Correlations of the 1/r^2 Model
• Spin dependent extension of Calogero-Sutherland model through anyon like representations of permutation operators
• Rationally-extended Dunkl oscillator on the line
• R-matrix-valued Lax pairs and long-range spin chains
• Quantum Lax pairs via Dunkl and Cherednik operators
• Calogero-Sutherland Type Models in Higher Dimensions
• Some Exactly Solvable Three-Body Problems in One dimension
• Trigonometric Cherednik algebra at critical level and quantum many-body problems
• Eigenfunctions for SU(N) particles with 1/r^2 interaction in harmonic confinement
• CFT approach to constraint operators for ($\beta$-deformed) hermitian one-matrix models
• Exactly-solvable system of one-dimensional trapped bosons with short and long-range interactions
• An exactly solvable supersymmetric spin chain of BC_N type
• Runge-Lenz vector in Calogero-Coulomb problem
• Novel correlations in two dimensions: Two-body problem
• Applications of the Collective Field Theory for the Calogero-Sutherland Model
• Quantum SU(2$|$1) supersymmetric Calogero-Moser spinning systems
• Notes on Collective Field Theory of Matrix and Spin Calogero Models
• Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model
• Free harmonic oscillators, Jack polynomials and Calogero-Sutherland systems
• Inozemtsev's hyperbolic spin model and its related spin chain
• Intertwining Relations for the Matrix Calogero-like Models: Supersymmetry and Shape Invariance
• Supertraces on the Algebras of Observables of the Rational Calogero Model with Harmonic Potential
• Geometric extensions of many-particle Hardy inequalities
• The $W_{1+\infty }$ effective theory of the Calogero- Sutherland model and Luttinger systems.
• Field theory of anyons in the lowest Landau level
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• Calogero model, deformed oscillators and the collapse
• On the Sutherland Spin Model of B_N Type and its Associated Spin Chain
• Algebraic Solution of the Hubbard Model on the Infinite Interval
• Generalized Calogero model in arbitrary dimensions
• On R-matrix valued Lax pairs for Calogero-Moser models
• Spherical Calogero model with oscillator/Coulomb potential: quantum case
• Solitons in a continuous classical Haldane-Shastry spin chain
• Exactly Solvable Models in Arbitrary Dimensions
• Exact ground states of quantum many-body systems under confinement
• Algebra of one-particle operators for the Calogero model
• Mapping the Calogero model on the Anyon model
• The Relativistic Linear Singular Oscillator
• Renormalized Harmonic-Oscillator Description of Confined Electron Systems with Inverse-Square Interaction
• Exact Results of the 1D $1/r^2$ Supersymmetric t-J Model without Translational Invariance
• PT -symmetric rational Calogero model with balanced loss and gain
• On the Hydrogen Atom via Wigner-Heisenberg Algebra
• Yangian-invariant field theory of matrix-vector models
• Jack polynomials with prescribed symmetry and hole propagator of spin Calogero-Sutherland model
• Integrable N-particle Hamiltonians with Yangian or Reflection Algebra Symmetry
• Observable algebra for the rational and trigonometric Euler Calogero Moser models
• Solvable scalar and spin models with near-neighbors interactions
• A Unified Algebraic Approach to Few and Many-Body Correlated Systems
• Universal Lax pairs for Spin Calogero-Moser Models and Spin Exchange Models
• Invariants of the $1/r^2$ Supersymmetric t-J Models
• A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems
• Exact Charge Dynamics in the Supersymmetric t-J Model with Inverse-Square Interaction
• q-def oscillator associated with Calogero model and its q-coherent state
• New Non-Symmetric Orthogonal Basis for the Calogero Model with Distinguishable Particles
• Cold Fermi-gas with long range interaction in a harmonic trap
• A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics
• A relativistic model of the isotropic three-dimensional singular oscillator
• Matrix oscillator and Calogero-type models
• Dynamical symmetry algebra of the Calogero model
• Nonlinear dynamics of spin and charge in spin-Calogero model
• Quantum Mechanics on Thin Cylinders
• Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models
• Integrable Models From Twisted Half Loop Algebras
• An infinite family of superintegrable Hamiltonians with reflection in the plane
• Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial
• Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
• Inequivalent Quantizations of the N = 3 Calogero model with Scale and Mirror-S_3 Symmetry
• On Spin Calogero-Moser system at infinity
• Multi-parameter deformed and nonstandard $Y(g{l}_M)$ Yangian symmetry in a novel class of spin Calogero-Sutherland models
• Integrable coupled Li$\acute{e}$nard-type systems with balanced loss and gain
• Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane
• Quantum Mechanics and Hidden Superconformal Symmetry
• A lecture on the Calogero-Sutherland models
• The asymptotic Bethe ansatz solution for one-dimensional SU(2) spinor bosons with finite range Gaussian interactions
• Orthogonality catastrophe and fractional exclusion statistics
• Non-Hermitian Oscillator and R-deformed Heisenberg Algebra
• Fractional Exclusion Statistics for the Multicomponent Sutherland Model
• $R$-matrices for the $n=2,3$ Elliptic Calogero-Moser Models
• Exchange operator formalism for N-body spin models with near-neighbors interactions
• Partition function for general multi-level systems
• One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable
• Confined quantum systems in one dimension and conductance oscillations in narrow channels
• On Some One-Parameter Families of Three-Body Problems in One Dimension: Exchange Operator Formalism in Polar Coordinates and Scattering Properties
• Green Function of the Sutherland Model with SU(2) internal symmetry
• Finite-difference representations of the degenerate affine Hecke algebra
• Self-Similar Potentials and q-Coherent States
• From Vertex Operators to Calogero-Sutherland Models
• On a dynamical symmetry group of the relativistic linear singular oscillator
• Noncommutative Fluids
• A One Dimensional Ideal Gas of Spinons, or Some Exact Results on the XXX Spin Chain with Long Range Interaction
• Duality in a hyperbolic interaction model integrable even in a strong confinement: Multi-soliton solutions and field theory
• Long Range Interaction Models and Yangian Symmetry
• Traces on the Algebra of Observables of Rational Calogero Model based on the Root System
• The q-Deformed Oscillator Representations and Their Coherent States of the su(1,1) Algebra
• Algebra of the observables in the Calogero model and in the Chern-Simons matrix model
• Interpretation and Extension of the Green's Ansatz for Paraparticles
• Algebra of Observables for Identical Particles in One Dimension
• Dunkl symplectic algebra in generalized Calogero models
• Comments on dihedral and supersymmetric extensions of a family of Hamiltonians on a plane
• Yangian Symmetries in the $SU(N{)}_1$ WZW Model and the Calogero-Sutherland Model
• Eigenvectors and scalar products for long range interacting spin chains II: the finite size effects
• Deformed Calogero--Moser operators and ideals of rational Cherednik algebras
• Anyons, Deformed Oscillator Algebras and Projectors
• Emptiness and Depletion Formation Probability in spin models with inverse square interaction
• Conserved charges of non-yangian type for the Frahm-Polychronakos spin chain
• Knizhnik-Zamolodchikov equations and the Calogero-Sutherland-Moser integrable models with exchange terms
• Algebraic study on the $A_{N-1}$- and $B_N$-Calogero models with bosonic, fermionic and distinguishable particles
• Sutherland Models for Complex Reflection Groups
• Hierarchies of Spin Models related to Calogero-Moser Models
• Coherent States and Geometric Phases in Calogero-Sutherland Model
• Interacting electrons in magnetic fields: Tracking potentials and Jastrow-product wavefunctions
• Inequivalent quantization of the rational Calogero model with a Coulomb type interaction
• Three-body generalization of the Sutherland model with internal degrees of freedom
• On Certain Quantum Deformations of $gl(N,R)$
• Continuous matrix-product states in inhomogeneous systems with long-range interactions
• Fermionic limit of the Calogero-Sutherland system
• Solutions to the Multi-Component 1/R Hubbard Model
• Symmetries of Spin Calogero Models
• New spin generalisation for long range interaction models
• Generalized Calogero-Moser systems from rational Cherednik algebras
• Exchange interactions, Yang-Baxter relations and transparent particles
• Deformed Algebras from Inverse Schwinger Method
• Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence
• On the solutions of multicomponent generalizations of the Lam{é} equation
• On symmetries of generalized Calogero model and Polychronakos-Frahm chain
• On the Infrared Limit of Two Dimensional QCD
• Calogero-Vasiliev Oscillator in Dynamically Evolving Curved Spacetime
• Exact Ground State of Several N-body Problems With an N-body Potential
• Jack-Laurent symmetric functions
• Cosine series quantum sampling method with applications in signal and image processing
• Conservation laws in the continuum $1/r^2$ systems
• Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials
• Integrabilities of the long range t-J model of twisted boundary condition
• Connection between the ideals generated by traces and by supertraces in the superalgebras of observables of Calogero models
• Universality of the R-deformed Heisenberg algebra
• Dunkl and Cherednik operators
• Quantum Integrable Systems in One Dimension
• Calogero model with Yukawa like interaction
• A Haldane-Shastry spin chain of BC_N type in a constant magnetic field
• Dynamical Properties of the 1/r^2-Type Supersymmetric t-J Model in a Magnetic Field: Manifestation of Spin-Charge Separation
• Exact Solution of Heisenberg-liquid models with long-range coupling
• Dunkl jump processes: relaxation and a phase transition
• Some spherical function values for two-row tableaux and Young subgroups with three factors
• Nonrelativistic Factorizable Scattering Theory of Multicomponent Calogero-Sutherland Model
• Calogero Model(s) and Deformed Oscillators
• On Hydrodynamic Correlations in Low-Dimensional Interacting Systems
• SU(m|n) supersymmetric Calogero-Sutherland model confined in harmonic potential
• Supertraces on the algebra of observables of the rational Calogero model based on the classical root system
• New algebraic structures in the $C_{\lambda }$-extended Hamiltonian system
• Generalized statistics and the algebra of observables
• Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials
• Multi-parameter deformed and nonstandard $Y(g{l}_M)$ Yangian symmetry in integrable variants of Haldane-Shastry spin chain
• Supersymmetric Calogero-Moser-Sutherland models: superintegrability structure and eigenfunctions
• Spectral Functions of Singular Operators
• Exact diagonalisation of 1-d interacting spinless Fermions
• Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid
• Coupling and particle number intertwiners in the Calogero model
• Jack polynomials with prescribed symmetry and some of their clustering properties
• Dynamical symmetries of the Calogero-Coulomb model
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models
• Matrix elements of vertex operators and fermionic limit of spin Calogero-Sutherland system
• Multiple-particle diffusion processes from the viewpoint of Dunkl operators: relaxation to the steady state
• A non-symmetric Yang-Baxter algebra for the quantum nonlinear Schrödinger model (PhD Thesis)
• Generalization of a result of Matsuo and Cherednik to the Calogero-Sutherland- Moser integrable models with exchange terms
• Deformed $C_{\lambda }$-Extended Heisenberg Algebra in Non-commutative Phase-Space
• Equivalence of the super Lax and local Dunkl operators for Calogero-like models
• A non-symmetric Yang-Baxter Algebra for the Quantum Nonlinear Schrödinger Model
• Parent Hamiltonians of Jastrow Wavefunctions
• Fermionic Matrix Models and Bosonization
• Positivity of Dunkl's intertwining operator