Let $(P,M,\pi)$ be a principal $G$-bundle, $\omega\in \mathbf \Omega^1(M,\mathfrak g)$ be a connection 1-form and $\Omega \in \mathbf \Omega^2(M,\mathfrak g)$ be its curvature 2-form, where $\mathfrak g$ is the Lie algebra of $G$. Let $\rho:G\to GL(F)$ be a Lie group representation over a finite dimensional vector space $F$ and denote by $(P\times_\rho F,M,\pi')$ the associated principal $G$-bundle by the representation $\rho$. The connection 1-form $\omega$ defines a covariant derivative $\nabla^\omega$ in the vector bundle $(P\times_\rho F,M,\pi')$.
Someone tolds me that this machinery is the underlying geometric setting for many Physical Theories (such as Classical Electromagnetism, Quantum Electrodynamics, etc):
(1) the elements of structural group $G$ represents all of the possible inner structure of a physical system (for example, the point charge in the $U(1)$-classical magnetic field)
(2) The sections of the associated vector bundle $P\times_\rho F$ can be viewed as wave functions $\psi:M\to F$ for the system (for example, the wave function $\psi:\mathbb R^3\to \mathbb C$ of a classical charged particle)
(3) And the covariant derivative $\nabla^\omega$ is commonly used for define a suitable evolution equation for the wave function (for example, the Schrödinger equation for the classical EM field)
I was wondering if there exits notes/references/articles in which I can find other physical examples from this geometric point of view (Quantum Chromodynamics, Quantum Electrodynamics, General Relativity, etc).
Thanks in advance