Related papers: Symplectic Groupoids and Poisson Electrodynamics
We define the gauge potentials of Poisson electrodynamics as sections of a symplectic realization of the spacetime manifold and infinitesimal gauge transformations as a representation of the associated Lie algebroid acting on the symplectic…
We formulate general definitions of semi-classical gauge transformations for noncommutative gauge theories in general backgrounds of string theory, and give novel explicit constructions using techniques based on symplectic embeddings of…
We introduce a new kind of groupoid--a pseudo \'etale groupoid, which provides many interesting examples of noncommutative Poisson algebras as defined by Block, Getzler, and Xu. Following the idea that symplectic and Poisson geometries are…
This paper develops new aspects of the interplay between shifted symplectic geometry and classical Poisson geometry, focusing on lagrangian morphisms into 2-shifted symplectic groups. We establish a Lie-type correspondence between such…
Poisson electrodynamics is the low-energy limit of a rank-one noncommutative gauge theory. It admits a closed formulation in terms of a Poisson structure on the space-time manifold and reproduces ordinary classical electrodynamics in the…
We investigate Snyder space-time and its generalizations, including Yang and Snyder-de-Sitter spaces, which constitute manifestly Lorenz invariant noncommutative geometries. This work initiates a systematic study of gauge theory on such…
Noticing that the space of the solutions of a first order Hamiltonian field theory has a pre-symplectic structure, we describe a class of conserved charges on it associated to the momentum map determined by any symmetry group of…
Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, it has become an independent field of research in…
We investigate the tension between symplecticity and gauge covariance in classical Hamiltonian mechanics. The pursuit of manifest covariance over manifest symplecticity results in a unique geometric formulation. Firstly, covariant yet…
Poisson electrodynamics is the semi-classical limit of $U(1)$ non-commutative gauge theory. It has been studied so far as a theoretical model, where an external field would be the source of the non-commutative effects in space-time. Being…
Lie-Poisson electrodynamics describes the semi-classical limit of non-commutative $U(1)$ gauge theory, characterized by Lie-algebra-type non-commutativity. We focus on the mechanics of a charged point-like particle moving in a given gauge…
We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems (as a (0 + 1)-dimensional…
We consider the problem of defining the field strength of abelian potentials when the spacetime is a Poisson manifold, within the groupoidal approach. The natural definition in terms of gauge invariant momenta is proved to be equivalent to…
We study metric-compatible Poisson structures in the semi-classical limit of noncommutative emergent gravity. Space-time is realized as quantized symplectic submanifold embedded in R^D, whose effective metric depends on the embedding as…
We construct a new model for relativistic particle on the noncommutative surface in $(2+1)$ dimensions, using the symplectic formalism of constrained systems and embedding the model on an extended phase space. We suggest a short cut to…
We discuss a version of Hamiltonian (2+1)-dimensional dynamics, in which one allows nonvanishing Poisson brackets also between the coordinates, and between the momenta. The resulting equations of motion are not any more derivable from a…
This note gives an overview on the construction of symplectic groupoids as reduced phase spaces of Poisson sigma models and its generalization in the infinite dimensional setting (before reduction).
We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the…
The Poisson gauge algebra is a semi-classical limit of complete non-commutative gauge algebra. In the present work we formulate the Poisson gauge theory which is a dynamical field theoretical model having the Poisson gauge algebra as a…
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…