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
describing combinations of energy E and momentum p allowed by classical special relativity for a particle of mass m; where 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 or simply as .
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; the propagator typically has singularities on the mass shell.
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.
Read more about this topic: On Shell And Off Shell
Famous quotes containing the words mass and/or shell:
“At first, he savored only the material quality of the sounds secreted by the instruments. And it had already been a great pleasure when, beneath the tiny line of the violin, slender, resistant, dense and driving, he noticed the mass of the piano’s part seeking to arise in a liquid splashing, polymorphous, undivided, level and clashing like the purple commotion of wave charmed and flattened by the moonlight.”
—Marcel Proust (1871–1922)
“Billy: You dropped some shell in there.
Ted: It’s all right. Makes it crunchier that way. You like French toast crunchy, don’t you?”
—Robert Benton (b. 1932)