Gaugeteori

Gaugeteori, or gauge theory, is a framework in physics and mathematics for describing fields and interactions that are invariant under local transformations of internal degrees of freedom, known as gauge symmetries. In physics, gauge theories model interactions as exchanges of gauge bosons, which arise to preserve local symmetry when matter fields interact with gauge fields.

At the core, the gauge principle requires that equations be invariant under local changes of certain internal parameters. To maintain this invariance one introduces gauge fields that couple to matter through covariant derivatives. The corresponding field strength, or curvature, encodes the interaction.

Electromagnetism is the simplest gauge theory, based on the abelian group U(1). Non-abelian gauge theories use groups such as SU(2) or SU(3), and Yang–Mills theory generalizes this structure. The Standard Model describes strong, weak, and electromagnetic interactions as SU(3)×SU(2)×U(1) gauge theory.

Mathematically, gauge theory is formulated with connections on principal bundles. The gauge field is a connection 1-form and the field strength is its curvature. Gauge transformations act by changing local trivializations, leaving physical observables invariant, linking to differential geometry and topology.

Historically, Weyl proposed gauge invariance in 1918, Yang and Mills extended it to non‑abelian symmetries in 1954, and subsequent developments led to quantum electrodynamics, quantum chromodynamics, and the electroweak theory. Gauge theory remains central to modern physics and to geometric analysis.