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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 ...
Historically, as a book-keeping device of covariant perturbation theory, the graphs were called Feynman–Dyson diagrams or Dyson graphs, [6] because the path integral was unfamiliar when they were introduced, and Freeman Dyson's derivation from old-fashioned perturbation theory borrowed from the perturbative expansions in statistical mechanics ...
In fact, BF theory can be used to formulate discrete gauge theory. One can add additional twist terms allowed by group cohomology theory such as Dijkgraaf – Witten topological gauge theory. [ 1 ] There are many kinds of modified BF theories as topological field theories , which give rise to link invariants in 3 dimensions, 4 dimensions, and ...
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 ...
Seiberg–Witten theory; Six-dimensional holomorphic Chern–Simons theory; Slavnov–Taylor identities; Soft photon; Stable Yang–Mills connection; Stable Yang–Mills–Higgs pair; Stueckelberg action; Supersymmetric gauge theory; Synthetic gauge field
Yang–Mills theory is a quantum field theory for nuclear binding devised by Chen Ning Yang and Robert Mills in 1953, as well as a generic term for the class of similar theories. The Yang–Mills theory is a gauge theory based on a special unitary group SU(n), or more generally any compact Lie group.
Gauge theory in mathematics should not be confused with the closely related concept of a gauge theory in physics, which is a field theory that admits gauge symmetry. In mathematics theory means a mathematical theory , encapsulating the general study of a collection of concepts or phenomena, whereas in the physical sense a gauge theory is a ...