Related papers: WKB expansion of Yang-Yang generating function and…
We consider, for $p$ odd, a $p$--brane coupled to a $(p+1)$th rank background antisymmetric tensor field and to background Yang-Mills (YM) fields {\it via} a Wess-Zumino term. We obtain the generators of antisymmetric tensor and Yang-Mills…
Using the Gitman-Lyakhovich-Tyutin generalization of the Ostrogradsky method for analyzing singular systems, we consider the Hamiltonian formulation of metric and tetrad gravities in two-dimensional Riemannian spacetime treating them as…
Dual Feynman rules for Dirac monopoles in Yang-Mills fields are obtained by the Wu-Yang (1976) criterion in which dynamics result as a consequence of the constraint defining the monopole as a topological obstruction in the field. The usual…
Baker constructed basic meromorphic functions on the Jacobian variety of a hyperelliptic curve with two points at infinity. We call them Baker functions. The construction is based on the Abel-Jacobi map, which allows us to identify the…
In this paper, Part II, of a two part paper we apply the results of [KW], Part I, to establish, with an explicit dual coordinate system, a commutative analogue of the Gelfand-Kirillov theorem for M(n), the algebra of $n\times n$ complex…
In this paper, we review the construction and large $N$ study of the continuous two-dimensional Yang--Mills theory with gauge group $\mathrm{U}(N)$ through probability, combinatorics and representation theory. In the first part, we define…
The notion of generating functions of Poisson structures was first studied in math.SG/0312380.They are special functions which induce, on open subsets of $\R^d$, a Poisson structure together with the local symplectic groupoid integrating…
In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the Hamilton-Jacobi equation. We use some well-known results…
We consider surfaces embedded in a Riemannian manifold of arbitrary dimension and prove that many aspects of their differential geometry can be expressed in terms of a Poisson algebraic structure on the space of smooth functions of the…
This is the second in a series of papers on Poisson formalism for the cubic nonlinear Schr\"{o}dinger equation with repulsive nonlinearity. In this paper we consider periodic potentials. The inverse spectral problem for the periodic…
The gauge action of the Lie group $G$ on the chiral WZNW phase space ${\cal M}_{\check G}$ of quasiperiodic fields with $\check G$-valued monodromy, where $\check G\subset G$ is an open submanifold, is known to be a Poisson-Lie (PL) action…
Several features of an analytic (infinite-dimensional) Grassmannian of (commensurable) subspaces of a Hilbert space were developed in the context of integrable PDEs (KP hierarchy). We extended some of those features when polarized separable…
The product of local operators in a topological quantum field theory in dimension greater than one is commutative, as is more generally the product of extended operators of codimension greater than one. In theories of cohomological type…
The moduli space of SL(2) flat connections on a punctured Riemann surface with the fixed conjugacy classes of the monodromies around the punctures is endowed with a system of holomorphic Darboux coordinates, in which the generating function…
This is a review of recent work on the chiral extensions of the WZNW phase space describing both the extensions based on fields with generic monodromy as well as those using Bloch waves with diagonal monodromy. The symplectic form on the…
Two methods of constructing 2D Toda $\tau$-functions that are generating functions for certain geometrical invariants of a combinatorial nature are related. The first involves generation of paths in the Cayley graph of the symmetric group…
This is the second paper of a series dedicated to the study of Poisson structures of compact types (PMCTs). In this paper, we focus on regular PMCTs, exhibiting a rich transverse geometry. We show that their leaf spaces are integral affine…
There is an emerging class of permutation factorization questions that cannot be expressed wholly in terms of the centre of the group algebra of the symmetric group. We shall term these non-central. A notable instance appears in recent work…
We prove that the isomonodromic tau function on a torus with Fuchsian singularities and generic monodromies in $GL(N,\mathbb{C})$ can be written in terms of a Fredholm determinant of Cauchy-Plemelj operators. We further show that the minor…
We review the role played by tau functions of special type - called {\it Bergman} tau functions in various areas: theory of isomonodromic deformations, solutions of Einstein's equations, theory of Dubrovin-Frobenius manifolds, geometry of…