Gauge theory

In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations.

Quotes

• The laws of physics can be made symmetric even under local gauge transformation in distance provided a gravitational field is introduced to compensate for the place-to-place variations. Physicists like to turn this statement around and say that the gravitational field is nature's way of maintaining a local gauge symmetry, a freedom to re-gauge the scale of distance arbitrarily from place to place. In the absence of gravity, there is only a global symmetry; we can transform only from one straight line path to another without distorting the physics. With gravity, we can transform to any shape of path whatever without changing the physics. A symmetry, remember, is the invariance of something under an operation. The symmetry involved here is the invariance of physics under arbitrary changes in the shape of a path of motion.
  • Paul Davies, Superforce: The Search for a Grand Unified Theory of Nature. Simon and Schuster. 1985. p. 114. ISBN 9780671605735.  (264 pages; 1st published in 1984)

• Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics. Gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in the early 1980's. Since the birth of the subject, it has retained its close connection with symplectic topology, a subject whose intricate structure was illuminated by Mikhail Gromov's introduction of pseudo-holomorphic curve techniques, also introduced in the early 1980's.
  • Clay Mathematics Institute. Summer School (2006). "Introduction by the editors, Ellwood, Ozsváth, Stipsicz, & Szabó". Floer Homology, Gauge Theory, and Low-dimensional Topology: Proceedings of the Clay Mathematics Institute 2004 Summer School, Alfréd Rényi Institute of Mathematics, Budapest, Hungary, June 5-26, 2004. American Mathematical Society. p. vii. ISBN 978-0-8218-3845-7. 

• ... gauge theories are the basis of interactions between elementary particles ... there are many books about gauge theories already out there – among the best are those written by Paul Frampton, J R Aitchison and Anthony Hey, Chris Quigg, Ta-Pei Cheng and Ling-Fong Li. ...
  ... quantum electrodynamics (QED) ... – despite its simplicity and limitations – serves as the mould of a gauge theory and at the same time it has a high predictive power and numerous applications.
  • Gilberto Tavares-Velasco, (22 September 2017) "review of An Introduction to Gauge Theories by Nicola Cabibbo, Luciano Maiani and Omar Benhar". CERN Courier.