相关论文: Canonical equivariant extensions using classical H…
We study the Euler-Lagrange cohomology and explore the symplectic or multisymplectic geometry and their preserving properties in classical mechanism and classical field theory in Lagrangian and Hamiltonian formalism in each case…
The classical Hamilton equations are reinterpreted by means of complex analysis, in a non standard way. This suggests a natural extension of the Hamilton equations to the quaternionic case, extension which coincides with the one introduced…
We determine the universal central extension of the Lie algebra of hamiltonian vector fields, thereby classifying its central extensions. Furthermore, we classify the central extensions of the Lie algebra of symplectic vector fields, of the…
We show that for a Hamiltonian action of a compact torus $G$ on a compact, connected symplectic manifold $M$, the $G$-equivariant cohomology is determined by the residual $S^1$ action on the submanifolds of $M$ fixed by codimension-1 tori.…
This text presents some basic notions in symplectic geometry, Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentum maps and their use for the reduction of Hamiltonian…
We construct a canonical extension for strong proximity lattices in order to give an algebraic, point-free description of a finitary duality for stably compact spaces. In this setting not only morphisms, but also objects may have distinct…
In this paper, we consider Sjamaar's holomorphic slice theorem, the birational equivalence theorem of Guillemin and Sternberg, and a number of important standard constructions that work for Hamiltonian circle actions in both the symplectic…
We give examples of symplectic actions of a cyclic group, inducing a trivial action on homology, on four-manifolds that admit Hamiltonian circle actions, and show that they do not extend to Hamiltonian circle actions. Our work applies…
Classical mechanical systems are modeled by a symplectic manifold $(M,\omega)$, and their symmetries, encoded in the action of a Lie group $G$ on $M$ by diffeomorphisms that preserves $\omega$. These actions, which are called "symplectic",…
A canonical formulation of coupled classical-quantum dynamics is presented. The theory is named symmetric hybrid dynamics. It is proved that under some general conditions its predictions are consistent with the full quantum ones. Moreover…
We outline the construction of invariants of Hamiltonian group actions on symplectic manifolds. These invariants can be viewed as an equivariant version of Gromov-Witten invariants. They are derived from solutions of a PDE involving the…
We construct a combinatorial invariant of Legendrian knots in standard contact three-space. This invariant, which encodes rational relative Symplectic Field Theory and extends contact homology, counts holomorphic disks with an arbitrary…
In this article we investigate whether a theory based on a classical Lagrangian for the minimal Standard-Model Extension (SME) can be quantized such that the result is equal to the corresponding low-energy Hamilton operator obtained from…
We describe extension classes arising in the $\ell$-adic and Hodge cohomology of Hilbert modular varieties, generalising results of Caspar to arbitrary dimensions. We show that this description is consistent with the "plectic conjectures"…
A compact symplectic manifold $(M, \omega)$ is said to satisfy the hard-Lefschetz condition if it is possible to develop an analogue of Hodge theory for $(M, \omega)$. This loosely means that there is a notion of harmonicity of differential…
It is shown how the canonical symmetry is used to look for the hierarchy of the Hamiltonian operators relevant to the system under consideration. It appears that only the invariance condition can be used to solve the problem.
The symmetries of the tree level string effective action are discussed. An appropriate effective action is constructed starting from the manifestly SL(2,R) invarint form of string effective action introduced by Schwarz and Sen. The…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
To any Hamiltonian action of a reductive algebraic group $G$ on a smooth irreducible symplectic variety $X$ we associate certain combinatorial invariants: Cartan space, Weyl group, weight and root lattices. For cotangent bundles our…
We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…