Related papers: Covariant Jacobi Brackets for Test Particles

The standard formulation of Jacobi manifolds in terms of differential operators on line bundles, although effective at capturing most of the relevant geometric features, lacks a clear algebraic interpretation similar to how Poisson algebras…

The covariant Poisson equation for Lie algebra-valued mappings defined in 3-dimensional Euclidean space is studied using functional analytic methods. Weighted covariant Sobolev spaces are defined and used to derive sufficient conditions for…

We examine the Wess-Zumino-Novikov-Witten (WZNW) model on a circle and compute the Poisson bracket algebra for left and right moving chiral group elements. Our computations apply for arbitrary groups and boundary conditions, the latter…

We classify Haag-dual Poincar\'e covariant subsystems $\B\subset \F$ of a graded-local net $\F$ on 4D Minkowski spacetime which satisfies standard assumptions and has trivial superselection structure. The result applies to the canonical…

We single out a class of Lagrangians on a group manifold, for which one can introduce non-canonical coordinates in the phase space, which simplify the construction of the Poisson structure without explicitly calculating the Dirac bracket.…

We introduce a bracket on 1-forms defined on ${\cal J}^{\infty}(S^1, \mathbb{R}^n)$, the infinite jet extension of the space of loops and prove that it satisfies the standard properties of a Poisson bracket. Using this bracket, we show that…

We extend the Poisson bracket from a Lie bracket of phase space functions to a Lie bracket of functions on the space of canonical histories and investigate the resulting algebras. Typically, such extensions define corresponding Lie algebras…

It is shown that the new formula for the field theory Poisson brackets arise naturally in the extension of the formal variational calculus incorporating divergences. The linear spaces of local functionals, evolutionary vector fields,…

We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The…

This paper is the second part of a series that develops the mathematical framework necessary for studying field theories on ``T-Minkowski'' noncommutative spacetimes. These spacetimes constitute a class of noncommutative geometries,…

We consider a hierarchy of Poisson structures defined on rational functions on the Riemann sphere. This hierarchy is originated in the theory of the integrable Camassa-Holm equation associated with the Krein's string spectral problem.…

In a preceding paper we introduced a notion of compatibility between a Jacobi structure and a Riemannian structure on a smooth manifold. We proved that in the case of fundamental examples of Jacobi structures : Poisson structures, contact…

While internal space-time symmetries of relativistic particles are dictated by the little groups of the Poincar\'e group, it is possible to construct representations of the little group for massive particles starting from harmonic…

It is well known that at distances shorter than Planck length, no length measurements are possible. The Volovich hypothesis asserts that at sub-Planckian distances and times, spacetime itself has a non-Archimedean geometry. We discuss the…

Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables…

The analysis of the covariant brackets on the space of functions on the solutions to a variational problem in the framework of contact geometry initiated in the companion letter Ref.19 is extended to the case of the multisymplectic…

We study the variances of the coordinates of an event considered as quantum observables in a Poincare' covariant theory. The starting point is their description in terms of a covariant positive-operator-valued measure on the Minkowski…

We extend the Jacobi structure from $TQ\times \mathbb{R}$ and $T^{*}Q \times \mathbb{R}$ to $A\times \mathbb{R}$ and $A^{*}\times \mathbb{R}$, respectively, where $A$ is a Lie algebroid and $A^{*}$ carries the associated Poisson structure.…

We generalize Poisson-Nijenhuis structures. We prove that on a manifold endowed with a Nijenhuis tensor and a Jacobi structure which are compatible, there is a hierarchy of pairwise compatible Jacobi structures. Furthermore, we study the…

The Tamari lattice and the associahedron provide methods of measuring associativity on a line. The real moduli space of marked curves captures the space of such associativity. We consider a natural generalization by considering the moduli…