相关论文: Large $N$ limit of integrable models

The integrability of the N-cosine model, a N-field generalization of the sine-Gordon model, is investigated. We establish to first order in conformal perturbation theory that, for arbitrary N, the model possesses a quantum conserved current…

We discuss the behavior of the Calogero model and the related model of deformed oscillators with the S_N extended Heisenberg algebra for a special value of the constant of interaction/statistical parameter nu. The problem with finite number…

We initiate a systematic study of integrable models for spin chains with constrained Hilbert spaces; we focus on spin-1/2 chains with the Rydberg constraint. We extend earlier results for medium-range spin chains to the constrained Hilbert…

Two dimensional classical integrable systems and different integrable deformations for them are derived from phase space realizations of classical $sl(2)$ Poisson coalgebras and their $q-$deformed analogues. Generalizations of Morse,…

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 examine the extent to which it is possible to realize the NMSSM "ideal Higgs" models espoused in several papers by Gunion et al in the context of partially universal GUT scale boundary conditions. To this end we use the powerful…

We present the complete one-loop corrected Higgs mass within the Standard Model. It is crucial to identify the observable mass as the renormalized one that depends on the external momentum. The correction is finite and dominated by the…

Motivated by Aganagic's equivariant mirror symmetry for certain Coulomb branches of a $3d$ $\mathcal{N}= 4$ gauge quiver theory, we would like to propose a set of ideas towards an extension of Aganagic's proposal to Hitchin systems. At the…

New boundary conditions for integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice are presented. These integrable extensions are formulated in terms of a generic XXX Heisenberg magnet interacting…

We discuss how a standard scattering theory a of multi-particle theory generalises to systems based on Hamiltonians that involve higher-order derivatives in their quantum mechanical formulation. As concrete examples, we consider Hamiltonian…

We study quantum intergrable systems of interacting particles from the point of view, proposed in our previous paper. We obtain Calogero-Moser and Sutherland systems as well their Ruijsenaars relativistic generalization by a Hamiltonian…

We identify dglas that control infinitesimal deformations of the pairs (manifold, Higgs bundle) and of Hitchin pairs. As a consequence, we recover known descriptions of first order deformations and we refine known results on obstructions.…

Ratner's theorem implies topological rigidity of immersed totally geodesic subspaces of noncompact type in finite-volume locally symmetric spaces. In higher rank and infinite volume, however, counter-examples to this rigidity have remained…

We show that the the generalized Calogero-Moser model with boundary potential of the P\"oschl-Teller type describes the non-relativistic limit of the quantum sine-Gordon model on a half-line with Dirichlet boundary condition.

It is noted that the internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles…

This review article discusses recent progress in understanding of various families of integrable models in terms of algebraic geometry, representation theory, and physics. In particular, we address the connections between soluble many-body…

The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical…

In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a…

In the framework of the two-loop renormalization group, the global profile of the Standard Model (SM) in its full parameter space is investigated up to the scale of the gauge singularity. The critical Higgs masses bordering the strong…

We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with $N$-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in…