Lagrangian submanifolds: open Gromov-Witten theory and Mirror Symmetry
Homotopy algebras, symplectic embeddings and non-commutative Gauge Theory
Problems of lagragian and Hamiltonian BRST quantization of Gauge theories
| Full text | |
| Author(s): |
Cabrera, Alejandro
;
Dherin, Benoit
Total Authors: 2
|
| Document type: | Journal article |
| Source: | INTERNATIONAL MATHEMATICS RESEARCH NOTICES; v. 2016, n. 7, p. 26-pg., 2016-01-01. |
| Abstract | |
We study the relationship between several constructions of symplectic realizations of a given Poisson manifold. Our main result is a general formula for a formal symplectic realization in the case of an arbitrary Poisson structure on R-n. This formula is expressed in terms of rooted trees and elementary differentials, building on the work of Butcher, and the coefficients are shown to be a generalization of Bernoulli numbers appearing in the linear Poisson case. We also show that this realization coincides with a formal version of the original construction of Weinstein, when suitably put in global Darboux form, and with the realization coming from tree-level part of Kontsevich's star product. We provide a simple iterated integral expression for the relevant coefficients and show that they coincide with underlying Kontsevich weights. (AU) | |
| FAPESP's process: | 10/19365-0 - Monoidal geometries |
| Grantee: | Benoit Richard Umbert Dherin |
| Support Opportunities: | Scholarships in Brazil - Young Researchers |
| FAPESP's process: | 10/15069-8 - Monoidal geometries |
| Grantee: | Benoit Richard Umbert Dherin |
| Support Opportunities: | Research Grants - Young Investigators Grants |