Momentum map
a tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action.
1. Idea. A momentum map is a dual incarnation of a Hamiltonian action of a Lie group (or Lie algebra) on a symplectic manifold. ... μ : X → g * .
INTRODUCTION TO THE MOMENT MAP 1. Symplectic Geometry 1 ...
Here ν(f) = Xf and. HamVF(M) denotes the space of Hamiltonian vector fields on (M,ω). Page 4. 4. JUAN CAMILO ORDUZ. 2. THE MOMENT MAP.
Intuition about Momentum Maps - Physics Stack Exchange
The moment map provides a coordinate-free description of how the Lie algebra of the symmetry embeds into the full Poisson algebra of observables.
The Momentum Map, Symplectic Reduction and an Introduction to ...
Let's now explicitely construct momentum maps for certain categories of symplectic manifolds. Definition 27 A momentum map J is said to be Ad∗-equivariant if ...
The moment map µ is G-equivariant if and only if the comoment map µ∗ : (g,[·,·]) → (C∞(M),{·,·}) is a Lie algebra homomorphism. Proof. First assume the G-action ...
Geometry of the momentum map - Mathematics
This is a map from the symplectic manifold to the dual of the. Lie algebra of the group acting on it. Historically, momentum maps and symplectic ...
Origin of the name ''momentum map'' - MathOverflow
The momentum map concept can be traced back to Sophus Lie's 1890 book, and is an English translation of the French words application moment.
SPDR Sector ETF Momentum Map | SSGA
The Sector ETF Momentum Map is a powerful tool that lets you see in real time how sectors are trending relative to their US, European and world benchmarks.
Momentum Mapping - an overview | ScienceDirect Topics
The main feature of the momentum map that makes it of interest for use in reduction is that it encodes conservation laws for G-symmetric Hamiltonian systems.
Share your videos with friends, family, and the world.
[2103.07670] The homotopy momentum map of general relativity
Abstract page for arXiv paper 2103.07670: The homotopy momentum map of general relativity.
Momentum Map-Submersion - Mathematics Stack Exchange
Momentum Map-Submersion ... Let (M,ω) be a symplectic manifold and G a Lie group acting hamiltonian on M, such that the momentum map Φ:M→g∗ is G- ...
Moment Maps From Lie Groups - ETH Zurich
Such a map is then called a moment map. We will show some properties of moment maps and also give several examples of hamiltonian actions.
[0705.0562] The momentum map in Poisson geometry - arXiv
Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum ...
Momentum Maps and Hamiltonian Reduction - SpringerLink
The present book offers a thorough description of reduction theory and a unified treatment of most of its developments and generalizations.
The moment maps we are interested in are equivariant with respect to the coadjoint action, that is, they satisfy Ad ∗ g ∘μ =μ∘g.
The Optimal Momentum Map | SpringerLink
The presence of symmetries in a Hamiltonian system usually simplies the existence of conservation laws that are represented mathematically in terms of the ...
Throughout M is a manifold, G is a Lie group and LG is the Lie algebra of G. Denote by Diff(M) the group of smooth self diffeomorphisms of M ...
The momentum map in Poisson geometry - Project MUSE
Momentum maps of Poisson actions. 3.1. Symplectization of a Poisson manifold. 3.2. From Poisson actions to Hamiltonian actions. 3.3. Examples. 4 ...