Gauge symmetries are essential for modern physics theories, but their status is unclear. This element reviews the current state of affairs on both the philosophy and physics sides, focusing on the circumstances in which the restriction of gauge theories to gauge invariant information is warranted. It also determines a set of questions to clarify the status of gauge symmetries.

Format: Paperback / softback
Publication date: 03 August 2023
Publisher: Cambridge University Press

Gauge symmetries play a crucial role in both the mathematical foundations and the conceptual construction of modern (particle) physics theories. However, the question remains whether they are a necessary component of theories or whether they can be eliminated. It is also unclear whether they serve as mere auxiliary tools to simplify calculations or whether they contain independent information. Therefore, their status, both in physics and the philosophy of physics, remains to be fully clarified. This Element provides a comprehensive review of the current state of affairs on both the philosophy and the physics sides. In particular, it focuses on the circumstances in which restricting 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 identify a set of unresolved questions that aim to clarify the status of gauge symmetries.

Gauge Symmetries in Modern Physics

Gauge symmetries are fundamental concepts in modern physics that play a central role in both the mathematical foundations and the conceptual construction of various physical theories. These symmetries are associated with the transformation properties of physical fields under certain gauge transformations, which are mathematical operations that modify the gauge parameters of a theory.

One of the most prominent examples of gauge symmetries is the electromagnetic gauge symmetry, which is associated with the electromagnetic field. In the standard model of particle physics, the electromagnetic gauge symmetry is broken down into three subgroups: the U(1) gauge group, the SU(2) gauge group, and the SU(3) gauge group. These subgroups correspond to different interactions between the electromagnetic field and other particles, such as the gauge bosons W and Z and the gauge fermions f and g.

Gauge symmetries also play a crucial role in the development of quantum field theories, which are the fundamental theories of particle physics. In these theories, the gauge symmetry is used to define the interactions between particles and to determine the behavior of physical phenomena. For example, in the standard model of quantum electrodynamics (QED), the gauge symmetry is used to define the interactions between electrons and photons and to explain the behavior of light and other electromagnetic radiation.

However, the status of gauge symmetries in modern physics is still a subject of ongoing debate and investigation. While gauge symmetries are widely accepted as a fundamental concept in physics, it is not yet clear whether they are a necessary component of all theories or whether they can be eliminated. Some physicists argue that gauge symmetries are essential for the consistency and predictability of physical theories, while others argue that they are merely an auxiliary tool to simplify calculations and that they do not contain independent information.

One of the key questions in the study of gauge symmetries is whether they can be eliminated or whether they are necessary for the existence of physical phenomena. In general, gauge symmetries can be eliminated by performing certain gauge transformations that modify the gauge parameters of a theory. However, it is not always possible to eliminate all gauge symmetries from a theory, and in some cases, it may be necessary to retain certain gauge symmetries to maintain the consistency and predictability of the theory.

Another important question is whether gauge symmetries contain independent information or whether they are merely an auxiliary tool to simplify calculations. While gauge symmetries can be useful for simplifying calculations, they can also provide insights into the underlying structure of physical theories and can help to identify new physical phenomena. For example, in the study of gauge theories in general relativity, gauge symmetries can be used to identify new types of gravitational interactions and to explain the behavior of black holes and other cosmic objects.

In conclusion, gauge symmetries play a crucial role in modern physics, both in the mathematical foundations and the conceptual construction of physical theories. While the status of gauge symmetries is still a subject of ongoing debate and investigation, it is clear that these symmetries are fundamental to the understanding of physical phenomena and that they will continue to play a vital role in the development of future physics theories.

ISBN-13: 9781009197229