Action (physics)

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. Action and the variational principle are used in Feynman's quantum mechanics and in general relativity. For systems with small values of action similar Planck's constant, quantum effects are significant.

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 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. Action has dimensions of energy × time or momentum × length, and its SI unit is joule-second (like the Planck constant h).