On shell and off shell
Configurations of a system that do or do not satisfy classical equations of motion / From Wikipedia, the free encyclopedia
In physics, particularly in quantum field theory, configurations of a physical system that satisfy classical equations of motion are called on the mass shell (on shell); while those that do not are called off the mass shell (off shell).
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In quantum field theory, virtual particles are termed off shell because they do not satisfy the energy–momentum relation; real exchange particles do satisfy this relation and are termed on (mass) shell.[1][2][3] In classical mechanics for instance, in the action formulation, extremal solutions to the variational principle are on shell and the Euler–Lagrange equations give the on-shell equations. Noether's theorem regarding differentiable symmetries of physical action and conservation laws is another on-shell theorem.