The hidden quantum origin of gauge connections

Abstract

A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on the fibre bundle, leading to an application of the quantum principles to the geometrical and topological definition of gauge theories. As a result, one could justifiably ask oneself if all interactions of the standard model, and perhaps even classical gravity have some quantum component after all. I employ a standard fibre bundle approach to introduce gauge theories, albeit it is known that a quantum bundle exists, simply because the main scope is to show that in the usual way in which we formulate classical gauge theories one can find quantum aspects that have been unknown until now. In a sense, I will try to justify the assessment that if we are to allow for gauge fields and parallel transport, we may have to allow at least some level of quantumness even in our classical gauge theories. The main statement is that propagation of interactions in spacetime is a quantum phenomenon. After writing the first draft of this article I noticed Y Shen C. Rosales-Guzman 2022 Laser & Photonics Reviews, 16,2100533 where the authors device entanglement of what they call ‘classical light’. This experiment supports my theoretical developments with the distinction that I interpret such phenomena also as fundamentally quantum. The distinction comes from the fact that the quantum nature of the experiments is manifested in a different way. My view on this is that there is no purely classical reality, no matter what the scale is at which we consider the description. I also discuss the fact that observing a quantum nature of ‘classical’ light propagation would amount to the requirement of modifying the causal structure defined in terms of the speed of light in a vacuum, on stronger grounds, based on the quantum interpretation of gauge connections.