Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches

Reviews the status of gauge symmetries, discusses symmetry breaking, and motivates and specifies gauge-invariant approaches to the Higgs mechanism.

This Element focuses on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance.Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. This Element reviews the current state of affairs on both the philosophy and the physics side. In particular, it focuses on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, the authors determine a set of yet to be answered questions to clarify the status of gauge symmetries.