# The principle of least action

• I
Homework Helper
Gold Member
TL;DR Summary
Does the principle of least action unifies physics in a way that we can say that all the fundamental laws of physics (e.g Newton's 2nd law, Maxwell's equations) we know. can be derived from the principle of least action?
From what I know Newton's 2nd law in classical mechanics can be derived from the principle of least action. Also from what I know, two of the Maxwell's equations (those that contain the time derivatives, i.e. Maxwell-Faraday law and Maxwell-Ampere law) also can be derived from the principle of least action. Of course the action defined is different in these two cases.

I don't know if this can be expanded in quantum physics and relativity, if also there the fundamental laws can be derived from the principle of minimizing some -depending on the case- action.

So is the principle of least action offering some sort of unification of the different branches of physics?

Gold Member
I have the textbook of Dirac on general relativity. There all kind of forces including electromagnetic and gravity are derived from corresponding terms of actions.

Classical version of action principle comes from quantum action principle or integral path method.

• atyy and Delta2
In QM, it has to be generalized to Feynman's path integral that sums over all paths. When doing the "saddle-point" approximation to the path integral, we recover the classical principle of extremizing the action.

• • fresh_42 and Delta2
Gold Member
As we all know...Physics is where the action is!

• hutchphd