"Classical" gauge theories (e.g. electrodynamics combined with quantum mechanics) have the following global description:
- $A_{\mu}$ is a connection in a principle bundle
- The matter fields are sections in an associated bundle
If one considers now "quantum" gauge theories (e.g. quantum electrodynamics) what is the global structure of the theory?
The four potential $A$ and the matter fields are now operator valued. Is it still possible to describe them as section of some kind of bundle?
