Final answer:
Gauge symmetries, specifically the U(1) symmetry group, explain mathematically how electromagnetic interactions occur. The U(1) symmetry is associated with the electromagnetic force and is described by the theory of quantum electrodynamics (QED). Equations like Ampère's law and Faraday's law include terms representing the U(1) gauge symmetry.
Step-by-step explanation:
In the field of particle physics, the electromagnetic interactions are explained mathematically by gauge symmetries. Specifically, the U(1) symmetry group is associated with the electromagnetic force. Gauge symmetries relate to the invariance of a physical theory under certain transformations. In the case of the U(1) symmetry, the electromagnetic force is described by the theory of quantum electrodynamics (QED).
Mathematically, electromagnetic interactions are described by equations such as Ampère's law and Faraday's law. These equations include terms that represent the gauge symmetry of the U(1) group.
The U(1) symmetry is associated with the conservation of electric charge. The interactions mediated by photons, which are the carrier particles of the electromagnetic force, are governed by the U(1) gauge symmetry.