The Ontology and Future of Gauge Theories

Modern physics is written in the language of gauge field theories. The Standard Model of particle physics is a gauge field theory, covering three of four known interactions. The Standard Model is a gauge theory in the sense that is rests on internal local symmetries. General relativity covers the other interaction, namely gravity. General relativity is a gauge theory in the sense that it rests on an external local symmetry. Since gauge symmetries play such a prominent role in modern physics, they more than deserve due conceptual reflection. The central topic of this project concerns the ontological status of gauge symmetries. Should they be interpreted as mere mathematical structure of our descriptions of reality or do they represent the structure of reality? There is some consensus among physicists and philosophers that gauge symmetries do not constitute symmetries of nature. They are not physically real but rather are mathematical redundancy that can be used to describe reality but does not represent structures of reality. Gauge symmetries have no direct empirical significance and physically real quantities must be gauge-invariant. However, if this is so, then we find worrisome conflicting assumptions at the very heart of modern particle physics. For instance, textbook approaches to the Higgs mechanism imply that the Higgs field gives mass to particles via the spontaneous symmetry breaking of a gauge symmetry. But how could the breaking of unphysical mathematical redundancy have any physical impact on our world? Furthermore, given the fact that each and every elementary field in the Standard Model is actually a gauge-variant quantity, this means that the fields/particles we typically consider the building blocks of reality cannot be physically real (because they are gauge-variant). Where does this leave us? The underlying thesis of this project is that such tensions and conceptual problems can be avoided by pursuing novel gauge- invariant approaches. It is the objective of this project to clarify the philosophical foundations of these approaches and to spell out the ontological implications. Furthermore, the project is expected to contribute to the development of such gauge-invariant approaches, thereby shedding light on new physics beyond the Standard Model and supporting research in quantum gravity.