Related papers: A Frame Bundle Generalization of Multisymplectic M…
Hamiltonian gravity, relying on arbitrary choices of "space," can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between "spatial" and "temporal" variables.…
In this paper we will explore fundamental constraints on the evolution of certain symplectic subvolumes possessed by any Hamiltonian phase space. This research has direct application to optimal control and control of conservative mechanical…
We build compact moduli spaces of Grassmannian framed bundles over a Riemann surface, essentially replacing a group by its bi-invariant compactification. We do this both in the algebraic and symplectic settings, and prove a…
Vlasov kinetic theory is the dynamics of a bunch of particles flowing according to symplectic Hamiltonian dynamics. More recently, this geometry has been extended to contact Hamiltonian dynamics. In this paper, we introduce geometric…
In this paper, we consider generalized moment maps for Hamiltonian actions on $H$-twisted generalized complex manifolds introduced by Lin and Tolman \cite{Lin}. The main purpose of this paper is to show convexity and connectedness…
We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than via mere representations of the structure group. We devise a notion of connection generalising Ehresmann…
Model of noncommutative gravity is constructed by means of Fedosov deformation quantization of endomorphism bundle. The fields describing noncommutativity -- symplectic form and symplectic connection -- are dynamical, and the resulting…
Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
A new approach to the model-independent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general…
We develop a framework based on the covariant phase space formalism that identifies gravitational edge modes as dynamical reference frames. They enable the identification of the associated spacetime region and the imposition of boundary…
A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems…
The presence of symmetries in a Hamiltonian system usually implies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or…
This paper introduces a geometric mechanics framework for constrained systems on principal bundles through \emph{compatible pairs} $(\mathcal{D}, \lambda)$, addressing fundamental challenges in gauge-constrained physical systems. We…
In this paper we will extend the notion of tangent bundle to a $\z$ graded tangent bundle. This graded bundle has a Lie algebroid structure and we can develop notions semi-riemannian metrics, Levi-civita connection, and curvature, on it. In…
This paper presents a unified approach to realize versatile distributed maneuvering with generalized formations. Specifically, we decompose the robots' maneuvers into two independent components, i.e., interception and enclosing, which are…
This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics…
This paper studies the application of multimomentum maps to the constraint analysis of general relativity on null hypersurfaces. It is shown that, unlike the case of spacelike hypersurfaces, some constraints which are second class in the…
We initiate the study of the norm-squared of the momentum map as a rigorous tool in infinite dimensions. In particular, we calculate the Hessian at a critical point, show that it is positive semi-definite along the complexified orbit, and…
This paper presents a generalization to image matching of the Hamiltonian approach for planar curve matching developed in the context of group of diffeomorphisms. We propose an efficient framework to deal with discontinuous images in any…