Related papers: A classical variant of the vertex algebra & the au…
We systematically derive the Lax pair formulation for both discrete and continuum integrable classical theories with consistent boundary conditions.
Derivations play a fundamental role in the definition of vertex (operator) algebras, sometimes regarded as a generalization of differential commutative algebras. This paper studies the role played by the integral counterpart of the…
Despite conventional wisdom that spin-1/2 systems have no classical analog, we introduce a set of classical coupled oscillators with solutions that exactly map onto the dynamics of an unmeasured electron spin state in an arbitrary,…
The mirror extensions for vertex operator algebras are studied. Two explicit examples which are not simple current extensions of some affine vertex operator algebras of type $A$ are given.
We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…
We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…
The notion of vertex operator coalgebra is presented and motivated via the geometry of conformal field theory. Specifically, we describe the category of geometric vertex operator coalgebras, whose objects have comultiplicative structures…
The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a…
The notion of vertex operator coalgebra is presented which corresponds to the family of correlation functions of one string propagating in space-time splitting into n strings in conformal field theory. This notion is in some sense dual to…
We study the classical dynamics of a particle in nonrelativistic Snyder-de Sitter space. We show that for spherically symmetric systems, parametrizing the solutions in terms of an auxiliary time variable, which is a function only of the…
We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra $\hat{\mathfrak{g}}$, from $\mathfrak{g}$-module homomorphisms. When…
We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories.…
We develop here a concept of deformed algebras through three examples and an application. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through formal series. We show how the example of…
The goal of this paper is to make the vertex operator algebra approach to mirror symmetry accessible to algebraic geometers. Compared to better-known approaches using moduli spaces of stable maps and special Lagrangian fibrations, this…
Starting with any R-matrix with spectral parameter, obeying the Yang-Baxter equation and a unitarity condition, we construct the corresponding infinite dimensional quantum group U_{R} in term of a deformed oscillators algebra A_R. The…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
We propose a regular way to construct lattice versions of $W$-algebras, both for quantum and classical cases. In the classical case we write the algebra explicitly and derive the lattice analogue of Boussinesq equation from the Hamiltonian…
In this paper we study certain vertex operator algebras associated to Jordan algebras and compute the correlation function of basic fields