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The concept and the name of gauge theory derives from the work of Hermann Weyl in 1918. [1] Weyl, in an attempt to generalize the geometrical ideas of general relativity to include electromagnetism, conjectured that Eichinvarianz or invariance under the change of scale (or "gauge") might also be a local symmetry of general relativity.
Gauge theory is dead! Long live gauge theory! (PDF - File, 95 kB), Notices of the AMS 42, March 1995, pp. 335–338 (on the Seiberg-Witten Theory) Topologie und Kombinatorik des Fußballs, Spektrum der Wissenschaft, 24 June 2006; Amorós, Jaume; Burger, Marc; Corlette, Kevin; Kotschick, Dieter; Toledo, Domingo (1996).
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]
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 ...
The ability to vary the gauge potential at different points in space and time (by changing (,)) without changing the physics is called a local invariance. Electromagnetic theory possess the simplest kind of local gauge symmetry called () (see unitary group). A theory that displays local gauge invariance is called a gauge theory.
A particular choice of the scalar and vector potentials is a gauge (more precisely, gauge potential) and a scalar function ψ used to change the gauge is called a gauge function. [ citation needed ] The existence of arbitrary numbers of gauge functions ψ ( r , t ) corresponds to the U(1) gauge freedom of this theory.
A gauge theory of elementary particles is a very attractive potential framework for constructing the Grand Unified Theory of physics. Such a theory has the very desirable property of being potentially renormalizable—shorthand for saying that all calculational infinities encountered can be consistently absorbed into a few parameters of the theory.
She won the 2019 Abel Prize for "her pioneering achievements in geometric partial differential equations, gauge theory, and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics." [9] She is the first, and so far only, woman to win the prize since its inception in 2003.