Editing On shell and off shell (section)

{{Short description|Configurations of a system that do or do not satisfy classical equations of motion}}
{{More citations needed|date=November 2014}}
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 particle]]s 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.<ref>Thomson, M. (2013). ''Modern particle physics''. Cambridge University Press, {{ISBN|978-1107034266}}, pp. 117–119.</ref><ref>{{Cite web|url=https://www.perimeterinstitute.ca/news/new-face-feynman-diagrams/deeper-dive-shell-and-shell|title=A Deeper Dive: On-Shell and Off-Shell|last=Cachazo|first=Freddy|date=Dec 21, 2012|website=Perimeter Institute for Theoretical Physics}}</ref><ref>{{cite arXiv|last=Arkani-Hamed|first=N.|date=Dec 21, 2012|title=Scattering Amplitudes and the Positive Grassmannian|class=hep-th|eprint=1212.5605}}</ref> In [[classical mechanics]] for instance, in the [[action (physics)|action]] formulation, extremal solutions to the [[variational principle]] are on shell and the [[Euler–Lagrange equation]]s give the on-shell equations. [[Noether's theorem]] regarding differentiable symmetries of physical action and [[conservation law]]s is another on-shell theorem.