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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.
Momentum mapping format is a key technique in the Material Point Method (MPM) for transferring physical quantities such as momentum, mass, and stress between a material point and a background grid. [1] The Material Point Method (MPM) is a numerical technique using a mixed Eulerian-Lagrangian description. It discretises the computational domain ...
The Dyson series can be alternatively rewritten as a sum over Feynman diagrams, where at each vertex both the energy and momentum are conserved, but where the length of the energy-momentum four-vector is not necessarily equal to the mass, i.e. the intermediate particles are so-called off-shell. The Feynman diagrams are much easier to keep track ...
For mechanical systems, the phase space usually consists of all possible values of the position and momentum parameters. It is the direct product of direct space and reciprocal space . [ clarification needed ] The concept of phase space was developed in the late 19th century by Ludwig Boltzmann , Henri Poincaré , and Josiah Willard Gibbs .
A schematic, or schematic diagram, is a designed representation of the elements of a system using abstract, graphic symbols rather than realistic pictures. A schematic usually omits all details that are not relevant to the key information the schematic is intended to convey, and may include oversimplified elements in order to make this essential meaning easier to grasp, as well as additional ...
In Newtonian mechanics, momentum (pl.: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. . It is a vector quantity, possessing a magnitude and a directi
Momentum map and reduction [ edit ] One of the principal ideas of geometric mechanics is reduction , which goes back to Jacobi's elimination of the node in the 3-body problem, but in its modern form is due to K. Meyer (1973) and independently J.E. Marsden and A. Weinstein (1974), both inspired by the work of Smale (1970).
Symbols, letters, numbers, ... A linear operator is a map that inputs a ket and outputs a ket. ... Angular momentum diagrams (quantum mechanics) ...