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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 shell'', and those that do not are called ''off shell''. In quantum field theory, virtual particles are termed off shell (mass-shell in this case) because they don't satisfy the Einstein energy-momentum relationship; real exchange particles do satisfy this relation and are termed on shell (mass-shell).〔Thomson, M. (2013). "Modern particle physics". Cambridge University Press, ISBN 978-1107034266 , p.117-119.〕 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 is also another on shell theorem. ==Mass shell== The term is a synonym for mass hyperboloid, meaning the hyperboloid in energy–momentum space describing the solutions to the equation: : which gives the energy ''E'' in terms of the momentum and the rest mass ''m'' of a particle in classical special relativity. The equation for the mass shell is also often written in terms of the four-momentum; in Einstein notation with metric signature (+,–,–,–) and units where the speed of light ''c'' = 1, as . In the literature, one may also encounter if the metric signature used is (–,+,+,+). 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. This is because the -dependence of the propagator is determined by the four-momenta of the incoming and outgoing particles. The propagator typically has singularities on the mass shell.〔Thomson, M. (2013). "Modern particle physics". Cambridge University Press, ISBN 978-1107034266 , p.119.〕 When speaking of the propagator, negative values for ''E'' that satisfy the equation are thought of as being on shell, though the classical theory does not allow negative values for the energy of a particle. This is because the propagator incorporates into one expression the cases in which the particle carries energy in one direction, and in which its antiparticle carries energy in the other direction; negative and positive on-shell ''E'' then simply represent opposing flows of positive energy. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「on shell and off shell」の詳細全文を読む スポンサード リンク
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