1. Gauge theory

    In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations. Formally, the Lagrangian is invariant under these transformations. The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field called the gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations. When such a theory is quantized, the quanta of the gauge fields are called gauge bosons. Wikipedia

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  2. en.wikipedia.org

    In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations ().Formally, the Lagrangian is invariant under these transformations.. The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in ...
  3. britannica.com

    Jan 20, 2025Gauge theory, class of quantum field theory, a mathematical theory involving both quantum mechanics and Einstein's special theory of relativity that is commonly used to describe subatomic particles and their associated wave fields. In a gauge theory there is a group of transformations of the field
    Author:The Editors of Encyclopaedia Britannica
  4. Learn the basics of gauge-theoretic approach to construction of invariants of manifolds, with examples of Seiberg-Witten gauge theory and Chern-Weil theory. The notes cover topics such as bundles and connections, Dirac operators, elliptic complexes, and Seiberg-Witten equations.
    Author:Andriy HaydysPublished:2019
  5. damtp.cam.ac.uk

    Learn the basics of non-Abelian gauge theories in four dimensions and other strongly coupled field theories in lower dimensions. The lecture notes cover topics such as electromagnetism, Yang-Mills, anomalies, lattice gauge theory, chiral symmetry breaking, large N, and quantum field theory in two and three dimensions.
  6. Gauge theory by now is a vast subject with many connections in geometry, analysis, and physics. In these notes I focus on gauge theory as it is used in the construction of manifolds invariants, other uses of gauge theory remain beyond the scope of these notes. The basic scheme of construction invariants of manifolds via gauge theory is quite ...
  7. cambridge.org

    The basics of gauge theories in two dimensions is "standard material" which appears in many books and review articles, for instance [66], [178], [1] and [2]. For treatment in non-covariant gauges see [28]. 8.1 Pure Maxwell theory The simplest theory of gauge fields in two dimensions is obviously the abelian
  8. harvest.aps.org

    A review of the history and evolution of gauge theory, from Weyl's unified theory of gravitation and electromagnetism to string theory and noncommutative geometry. The article covers the concepts of gauge invariance, dimensional reduction, fiber bundles, and the standard model.

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