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| {{Unreferenced|date=December 2009}}
| | Wholesaler Dee Sanderford from Moose Creek, has pastimes such as motorbikes, diet and yoyo. Last month very recently traveled to Historic Monuments of Ancient Kyoto (Kyoto. |
| {{expert-subject|Physics}}
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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'''''.
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| For instance, in [[classical mechanics]] in the [[action (physics)|action]] formulation, extremal solutions to the [[variational principle]] are on shell and the [[Euler-Lagrange equation]]s are on shell equations (i.e., they do not hold off shell). [[Noether's theorem]] is also another on shell theorem.
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| ==Mass shell==
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| The term comes from the phrase '''mass shell''', which is a synonym for '''mass hyperboloid''', meaning the [[hyperboloid]] in [[energy]]-[[momentum]] space describing the solutions to the equation
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| :<math>E^2 - |\vec{p} \,|^2 c^2 = m^2 c^4</math>
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| describing combinations of energy ''E'' and momentum ''p'' allowed by classical [[special relativity]] for a particle of mass ''m''; where <math>c</math> is the [[speed of light]]. The equation for the mass shell is also often written in terms of the [[four-momentum]], in [[Einstein notation]] and units where ''c'' = 1, as <math>p^\mu p_\mu = m^2</math> or simply as <math>p^2 = m^2</math>.
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| [[Virtual particles]] corresponding to internal [[propagator]]s 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; the propagator typically has [[mathematical singularity|singularities]] on the mass shell.
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| 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.
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| {{DEFAULTSORT:On Shell And Off Shell}}
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| [[Category:Quantum field theory]]
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Wholesaler Dee Sanderford from Moose Creek, has pastimes such as motorbikes, diet and yoyo. Last month very recently traveled to Historic Monuments of Ancient Kyoto (Kyoto.