相关论文: Poisson sigma models and symplectic groupoids

In this paper, we study half-densities enhancing the multiplication map on a symplectic groupoid and which satisfy a suitable associativity condition. This is structurally motivated by the expected complete semiclassical-analytic…

We introduce a new class of Poisson structures on a Riemannian manifold. A Poisson structure in this class will be called a Killing-Poisson structure. The class of Killing-Poisson structures contains the class of symplectic structures, the…

We consider some differential geometric classes of local and nonlocal Poisson and symplectic structures on loop spaces of smooth manifolds which give natural Hamiltonian and multihamiltonian representations for some important nonlinear…

We establish a link between the multisymplectic and the covariant phase space approach to geometric field theory by showing how to derive the symplectic form on the latter, as introduced by Crnkovic-Witten and Zuckerman, from the…

We present a general definition of the Poisson bracket between differential forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories and, more generally, on exact multisymplectic…

We generalize the $(n+1)$-dimensional twisted $R$-Poisson topological sigma model with flux on a target Poisson manifold to a Lie algebroid. Analyzing consistency of constraints in the Hamiltonian formalism and the gauge symmetry in the…

In this article, we first introduce the notion of a {\it continuous cover} of a manifold parametrised by any compact manifold endowed with a mass 1 volume-form. We prove that any such cover admits a partition of unity where the usual sum is…

Symplectic and Poisson structures of certain moduli spaces/Huebschmann,J./ Abstract: Let $\pi$ be the fundamental group of a closed surface and $G$ a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a…

We prove a normal form theorem for principal Hamiltonian actions on Poisson manifolds around the zero locus of the moment map. The local model is the generalization to Poisson geometry of the classical minimal coupling construction from…

We describe the symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds. Using the two dimensional sphere ($S^2$) and disc ($D^2$) as illustrative cases, we write their path integral representations using…

We show that symplectic forms taming complex structures on compact manifolds are related to special types of almost generalized K\"ahler structures. By considering the commutator $Q$ of the two associated almost complex structures…

We extend the problem of finding Hamiltonian-invariant volume forms on a Poisson manifold to the problem of construction of Hamiltonian-invariant generalized functions. For this we introduce the notion of generalized center of a Poisson…

Let R be a commutative ring, and let A be a Poisson algebra over R. We construct an (R,A)-Lie algebra structure, in the sense of Rinehart, on the A-module of K\"ahler differentials of A depending naturally on A and the Poisson bracket. This…

Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold ("phase space"). His algorithm gives a non-commutative, but…

Superanalysis can be deformed with a fermionic star product into a Clifford calculus that is equivalent to geometric algebra. With this multivector formalism it is then possible to formulate Riemannian geometry and an inhomogeneous…

The Poisson--Weil sigma model, worked out by us recently, stems from gauging a Hamiltonian Lie group symmetry of the target space of the Poisson sigma model. Upon gauge fixing of the BV master action, it yields interesting topological field…

After a brief description of the $\mathbb{Z}$-graded differential Poisson algebra, we introduce a covariant star product for exterior differential forms and give an explicit expression for it up to second order in the deformation parameter…

We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves…

Symplectic manifolds which are homogeneous spaces of Poisson-Lie groups are studied in this paper. We show that these spaces are, under certain assumptions, covering spaces of dressing orbits of the Poisson-Lie groups which act on them. The…

As a detailed application of the BV-BFV formalism for the quantization of field theories on manifolds with boundary, this note describes a quantization of the relational symplectic groupoid for a constant Poisson structure. The presence of…