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A momentum map is often also required to be -equivariant, where acts on via the coadjoint action, and sometimes this requirement is included in the definition of a Hamiltonian group action. If the group is compact or semisimple, then the constant of integration can always be chosen to make the momentum map coadjoint equivariant.
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 ...
A plot of position and momentum variables as a function of time is sometimes called a phase plot or a phase diagram. However the latter expression, " phase diagram ", is more usually reserved in the physical sciences for a diagram showing the various regions of stability of the thermodynamic phases of a chemical system, which consists of ...
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 ...
To map the band structure over a two-dimensional momentum space, the sample is rotated while keeping the light spot on the surface fixed. The most common choice is to change the polar angle θ around the axis that is parallel to the slit and adjust the tilt τ or azimuth φ so emission from a particular region of the Brillouin zone can be reached.
The four-momentum of the virtual particle is the difference between the four-momenta of the incoming and outgoing particles. Virtual particles corresponding to internal propagators in a Feynman diagram are in general allowed to be off shell, but the amplitude for the process will diminish depending on how far off shell they are. [ 4 ]
A diagram that is not a forest diagram is called a loop diagram, and an example is one where two lines of an X are joined to external lines, while the remaining two lines are joined to each other. The two lines joined to each other can have any momentum at all, since they both enter and leave the same vertex.
If P is the phase space and G the symmetry group, the momentum map is a map :, and the reduced spaces are quotients of the level sets of J by the subgroup of G preserving the level set in question: for one defines = /, and this reduced space is a symplectic manifold if is a regular value of J.