Configurations of a system that do or do not satisfy classical equations of motion
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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).
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.
^Thomson, M. (2013). Modern particle physics. Cambridge University Press, ISBN 978-1107034266, pp. 117–119.
^Cachazo, Freddy (Dec 21, 2012). "A Deeper Dive: On-Shell and Off-Shell". Perimeter Institute for Theoretical Physics.
^Arkani-Hamed, N. (Dec 21, 2012). "Scattering Amplitudes and the Positive Grassmannian". arXiv:1212.5605 [hep-th].
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