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.