Action (physics)

Action
Common symbols	S
SI unit	joule-second
Other units	J⋅Hz−1
In SI base units	kg⋅m2⋅s−1
Dimension	${\displaystyle {\mathsf {M}}\cdot {\mathsf {L}}^{2}\cdot {\mathsf {T}}^{-1}}$

In physics, action is a scalar quantity that describes how the balance of kinetic versus potential energy of a physical system changes with trajectory. Action is significant because it is an input to the principle of stationary action, an approach to classical mechanics that is simpler for multiple objects.^[1] Action and the variational principle are used in Feynman's quantum mechanics^[2] and in general relativity.^[3] For systems with small values of action similar to the Planck constant, quantum effects are significant.^[4]

In the simple case of a single particle moving with a constant velocity (thereby undergoing uniform linear motion), the action is the momentum of the particle times the distance it moves, added up along its path; equivalently, action is the difference between the particle's kinetic energy and its potential energy, times the duration for which it has that amount of energy.

More formally, action is a mathematical functional which takes the trajectory (also called path or history) of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths.^[5] Action has dimensions of energy × time or momentum × length, and its SI unit is joule-second (like the Planck constant h).^[6]