In mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map[1]) is a tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action. The momentum map generalizes the classical notions of linear and angular momentum. It is an essential ingredient in various constructions of symplectic manifolds, including symplectic (Marsden–Weinstein) quotients, discussed below, and symplectic cuts and sums.
^Moment map is a misnomer and physically incorrect. It is an erroneous translation of the French notion application moment. See this mathoverflow question for the history of the name.
mathematics, specifically in symplectic geometry, the momentummap (or, by false etymology, moment map) is a tool associated with a Hamiltonian action of...
physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important...
quantities are the components of the momentummap J. If P is the phase space and G the symmetry group, the momentummap is a map J : P → g ∗ {\displaystyle \mathbf...
mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a...
photoemission angular distribution maps, so-called tomograms (also known as momentummaps or k {\displaystyle k} -maps), to reveal information about the...
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism...
dual of g ) {\displaystyle {\mathfrak {g}})} a regular value of the momentummap Φ : M → g ∗ {\displaystyle \Phi :M\to {\mathfrak {g}}^{*}} . Let M 0...
_{n+1}-\theta _{n}} for the standard map, the equations reordered to emphasize similarity. In essence, the circle map forces the momentum to a constant. Ushiki's theorem...
{O}}_{\mu },\omega )} is a Hamiltonian G {\displaystyle G} -action with momentummap given by the inclusion O μ ↪ g ∗ {\displaystyle {\mathcal {O}}_{\mu }\hookrightarrow...
the four-momentum (also called 4-momentum) is also called the energy–momentum 4-vector. Using an uppercase P to represent the four-momentum and a lowercase...
quantum angular momentum efficiently, given that map’s ease of organizing the (symmetric) representations of su(2) in Fock space. The map utilizes several...
reference map frame (used to define simultaneity) and proper time τ elapsed on the clocks of the traveling object. It equals the object's momentum p divided...
2013. Bursztyn, Henrique; Crainic, Marius (2005). "Dirac structures, momentummaps, and quasi-Poisson manifolds". The Breadth of Symplectic and Poisson...
space to which is associated a bilinear map V × W → V ⊗ W {\displaystyle V\times W\rightarrow V\otimes W} that maps a pair ( v , w ) , v ∈ V , w ∈ W {\displaystyle...
to rotate around an axis, torque must be applied to change its angular momentum. The amount of torque needed to cause any given angular acceleration (the...
ISBN 3-7643-3103-8 Gotay, M.J., Isenberg, J., Marsden, J.E., Montgomery R., MomentumMaps and Classical Fields Part I: Covariant Field Theory, November 2003...
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