Related papers: Hamiltonian Analysis of Doubled 4d Chern-Simons
In this paper we study a quadratic Poisson algebra structure on the space of bilinear forms on $C^{N}$ with the property that for any $n,m\in N$ such that $n m =N$, the restriction of the Poisson algebra to the space of bilinear forms with…
Configuration spaces of many real mechanical systems appear to be manifolds with singularity. A singularity often indicates that geometry of motion may change at the singular point of configuration space. We face conceptual problem…
We introduce and study a notion of analytic loop group with a Riemann-Hilbert factorization relevant for the representation theory of quantum affine algebras at roots of unity with non trivial central charge. We introduce a Poisson…
A wide class of Hamiltonian systems with N degrees of freedom and endowed with, at least, (N-2) functionally independent integrals of motion in involution is constructed by making use of the two-photon Lie-Poisson coalgebra. The set of…
We study the $\lambda$--deformation of symmetric coset models from the viewpoint of a four dimensional Chern-Simons theory \cite{CY3}. In addition, by applying the "dual" boundary conditions of the ones used in the construction…
We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms…
We revisit and construct new examples of supersymmetric 2D topological sigma models whose target space is a Poisson supermanifold. Inspired by the AKSZ construction of topological field theories, we follow a graded-geometric approach and…
We study four-point functions in Chern-Simons vector models in the large $N$ limit. We compute the four-point function of the scalar primary to all orders in the `t Hooft coupling $\lambda=N/k$ in $U(N)_k$ Chern-Simons theory coupled to a…
3d Chern-Simons gauge theory has a strong connection with 2d CFT and link invariants in knot theory. We impose some constraints on the $D(2|1;\alpha)$ CS theory in the similar context of the hamiltonian reduction of 2d superconformal…
We formulate Poisson Chern-Simons gauge theories on compact group manifolds. These describe a sector of the large representation limit of noncommutative Chern-Simons in the same way as the light-cone formulation of the membrane action…
We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group $G$ and a…
It is shown that the variety of transposed Poisson algebras coincides with the variety of Gelfand-Dorfman algebras in which the Novikov multiplication is commutative. The Gr\"obner-Shirshov basis for the transposed Poisson operad is…
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…
We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…
The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real…
A new class of two dimensional integrable field theories, based on the mathematical notion of Poisson manifolds, and containing gravity-Yang-Mills systems as well as the G/G gauged Wess-Zumino Witten-model, are presented. The local…
We discuss a generalization of Chern-Simons theory in three dimensions based on Leibniz (or Loday) algebras, which are generalizations of Lie algebras. Special cases of such theories appear in gauged supergravity, where the Leibniz algebra…
We describe a 3d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 3d spatial lattice to a 2-form $\mathbb{Z}_2$ gauge theory with an unusual Gauss law. An important property of this map is that it…
The canonical quantization of a field theory for spin-$1/2$ massive bosons that satisfy the Klein-Gordon equation is presented. The breakdown of the usual spin-statistics connection is due to the redefinition of the dual field, rendering…
Construction of integrable field theories in space with a boundary is extended to fermionic models. We obtain general forms of boundary interactions consistent with integrability of the massive Thirring model and study the duality…