131 citations · 1.2k across the 53 of their papers we have counts for
24 papers · 1 filter
Spin Calogero-Moser periodic chains and two dimensional Yang-Mills theory with corners
Nicolai Reshetikhin
Quantum Calogero-Moser spin system is a superintegable system with the spectrum of commuting Hamiltonians that can be described entirely in terms of representation theory of corres…
Periodic and open classical spin Calogero-Moser chains
Nicolai Reshetikhin
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…
Integrability of Limit Shapes of the Inhomogeneous Six Vertex Model
David Keating, Nicolai Reshetikhin, Ananth Sridhar
In this paper we prove that the Euler-Lagrange equations for the limit shape for the inhomogeneous six vertex model on a cylinder have infinitely many conserved quantities.
Superintegrable Systems on Moduli Spaces of Flat Connections
S. Arthamonov, N. Reshetikhin
The main result of this paper is the construction of a family of superintegrable Hamiltonian systems on moduli spaces of flat connections on a principle -bundle on a surface. Th…
Poisson sigma model and semiclassical quantization of integrable systems
Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin
In this paper we outline the construction of semiclassical eigenfunctions of integrable models in terms of the semiclassical path integral for the Poisson sigma model with the targ…
Semiclassical geometry of integrable systems
Nicolai Reshetikhin
The main result of this paper is a formula for the scalar product of semiclassical eigenvectors of two integrable systems on the same symplectic manifold. An important application…
Superintegrability of Generalized Toda Models on Symmetric Spaces
Nicolai Reshetikhin, Gus Schrader
In this paper we prove superintegrability of Hamiltonian systems generated by functions on , restriced to a symplectic leaf of the Poisson variety , where …
Limit Shapes of the Stochastic Six Vertex Model
Nicolai Reshetikhin, Ananth Sridhar
We show that limit shapes for the stochastic 6-vertex model on a cylinder with the uniform boundary state on one end are solutions to the Burger type equation. Solutions to these e…
Perturbative BV theories with Segal-like gluing
Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin
This is a survey of our program of perturbative quantization of gauge theories on manifolds with boundary compatible with cutting/pasting and with gauge symmetry treated by means o…
Integrability of Limit Shapes of the Six Vertex Model
Nicolai Reshetikhin, Ananth Sridhar
The main result of this paper is the construction of infinitely many conserved quantities (corresponding to commuting transfer-matrices) for the limit shape equation for the 6-vert…
Degenerately Integrable Systems
Nicolai Reshetikhin
The subject of this paper is degenerate integrability in Hamiltonian mechanics. It starts with a short survey of degenerate integrability. The first section contains basic notions.…
Perturbative quantum gauge theories on manifolds with boundary
Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin
This paper introduces a general perturbative quantization scheme for gauge theories on manifolds with boundary, compatible with cutting and gluing, in the cohomological symplectic…
Combinatorial Quantum Field Theory and Gluing Formula for Determinants
Nicolai Reshetikhin, Boris Vertman
We define the combinatorial Dirichlet-to-Neumann operator and establish a gluing formula for determinants of discrete Laplacians using a combinatorial Gaussian quantum field theory…
Semiclassical quantization of classical field theories
Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin
These lectures are an introduction to formal semiclassical quantization of classical field theory. First we develop the Hamiltonian formalism for classical field theories on space…
Classical and quantum Lagrangian field theories with boundary
Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin
This note gives an introduction to Lagrangian field theories in the presence of boundaries. After an overview of the classical aspects, the cohomological formalisms to resolve sing…
Classical BV theories on manifolds with boundary
Aberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin
In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV co…
Lectures on the integrability of the 6-vertex model
N. Reshetikhin
This is an overview of various aspects of the 6-vertex model in statistical mechanics and related models.
The 6-vertex model with fixed boundary conditions
K. Palamarchuk, N. Reshetikhin
We study the 6-vertex model with fixed boundary conditions. In the thermodynamical limit there is a formation of the limit shape. We collect most of the known results about the ana…
Lectures on quantization of gauge systems
N. Reshetikhin
A gauge system is a classical field theory where among the fields there are connections in a principal G-bundle over the space-time manifold and the classical action is either inva…
On domain wall boundary conditions for the XXZ spin Hamiltonian
Domenico Orlando, Susanne Reffert, Nicolai Reshetikhin
In this note, we derive the spectrum of the infinite quantum XXZ spin chain with domain wall boundary conditions. The eigenstates are constructed as limits of Bethe states for the…
Random skew plane partitions with a piecewise periodic back wall
Cedric Boutillier, Sevak Mkrtchyan, Nicolai Reshetikhin +1
Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes. In the present work we consider the limit of large r…
Asymptotic shapes with free boundaries
P Di Francesco, N. Reshetikhin
We study limit shapes for dimer models on domains of the hexagonal lattice with free boundary conditions. This is equivalent to the large deviation phenomenon for a random stepped…
Dimers on surface graphs and spin structures. II
David Cimasoni, Nicolai Reshetikhin
In a previous paper, we showed how certain orientations of the edges of a graph G embedded in a closed oriented surface S can be understood as discrete spin structures on S. We the…
Dimers on surface graphs and spin structures. I
David Cimasoni, Nicolai Reshetikhin
Partition functions for dimers on closed oriented surfaces are known to be alternating sums of Pfaffians of Kasteleyn matrices. In this paper, we obtain the formula for the coeffic…