I have a question about the meaning of Yang-Mills Functional.


It is stated everywhere that the Yang-Mills Functional is a measure of energy. But the formal definition of the Yang-Mills Functional is:


* To have a manifold $M$ together with a smooth vector bundle $E\longrightarrow M$
* To a given connection $A$ over $E\longrightarrow M$, the Yang-Mills Functional assigns the integral of the norm of the curvature of $A$.


I understand the mathematical background, but **why does it represent *energy*?** Is there any intuitive way to explain this link?


Any idea or suggestion is welcome.



Yang-Mills Functional and Energy
The easiest way to see that the norm of the curvature corresponds to the energy is to consider the special case of an abelian U(1)-Yang-Mills theory (i.e. electrodynamics). If you write out the norm squared of the curvature in terms of the $E$ and $B$ fields you get the expression $E^2 + B^2$. This is exactly the familiar energy density of an electrodynamic field, see for example [wikipedia](http://en.wikipedia.org/wiki/Electric_field#Energy_in_the_electric_field).


