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A gauge theory is a type of theory in physics. The word gauge means a measurement , a thickness, an in-between distance (as in railroad tracks ), or a resulting number of units per certain parameter (a number of loops in an inch of fabric or a number of lead balls in a pound of ammunition ). [ 1 ]
The "gauge covariant" version of a gauge theory accounts for this effect by introducing a gauge field (in mathematical language, an Ehresmann connection) and formulating all rates of change in terms of the covariant derivative with respect to this connection. The gauge field becomes an essential part of the description of a mathematical ...
In this sense it is a 'master theory' for integrable systems, allowing many known systems to be recovered by picking appropriate parameters, such as choice of gauge group and symmetry reduction scheme. Other such master theories are four-dimensional Chern–Simons theory and the affine Gaudin model.
In theoretical physics, the notion of gauge symmetries depending on parameter functions is a cornerstone of contemporary field theory. A gauge symmetry of a Lagrangian L {\displaystyle L} is defined as a differential operator on some vector bundle E {\displaystyle E} taking its values in the linear space of (variational or exact) symmetries of ...
Chern–Simons theory is a gauge theory, which means that a classical configuration in the Chern–Simons theory on M with gauge group G is described by a principal G-bundle on M. The connection of this bundle is characterized by a connection one-form A which is valued in the Lie algebra g of the Lie group G.
In quantum field theory, Wilson loops are gauge invariant operators arising from the parallel transport of gauge variables around closed loops.They encode all gauge information of the theory, allowing for the construction of loop representations which fully describe gauge theories in terms of these loops.
In this case, the quiver gauge theory is a four-dimensional = supersymmetric gauge theory. The quiver gauge theory in higher dimensions can be defined similarly. The quiver is particularly convenient for representing conformal gauge theory. The structure of the quiver makes it easy to check whether the theory preserves conformal symmetry.
A gauge group is a group of gauge symmetries of the Yang–Mills gauge theory of principal connections on a principal bundle. Given a principal bundle P → X {\displaystyle P\to X} with a structure Lie group G {\displaystyle G} , a gauge group is defined to be a group of its vertical automorphisms, that is, its group of bundle automorphisms.