On Shell and Off Shell

On Shell And Off Shell

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.

For instance, in classical mechanics in the action formulation, extremal solutions to the variational principle are on shell and the Euler-Lagrange equations are on shell equations (i.e., they do not hold off shell). Noether's theorem is also another on shell theorem.