Gauge theory

Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. Gauge theories with non-Abelian symmetry groups are also sometimes known as Yang-Mills theories. Most physical theories are described by Lagrangians which are invariant under certain transformations, when the transformations are identically performed at every space-time point—they have global symmetries. Gauge theory extends this idea by requiring that the Lagrangians must possess local symmetries as well—it should be possible to perform these symmetry transformations in a particular region of space-time without affecting what happens in another region. This requirement is a generalized version of the equivalence principle of general relativity.

Related Topics:
Symmetry transformation - Abelian - Lagrangian - Invariant - Space-time - Point - Equivalence principle - General relativity

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The importance of gauge theories for physics stems from the tremendous success of the mathematical formalism in providing a unified framework to describe the quantum field theories of electromagnetism, the weak force and the strong force. This theory, known as the Standard Model, accurately describes experimental predictions regarding three of the four fundamental forces of nature, and is a gauge theory with the gauge group SU(3) × SU(2) × U(1). Modern theories like string theory, as well as some formulations of general relativity, are in one way or another, gauge theories.

Related Topics:
Quantum field theories - Electromagnetism - Weak force - Strong force - Standard Model - Experiment - Fundamental force - Gauge group - SU(3) × SU(2) × U(1) - String theory - Some formulations - General relativity

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Sometimes, the term gauge symmetry is used in a more general sense to include any local symmetry, like for example, diffeomorphisms. This sense of the term will not be used in this article.

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