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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 ...
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. Gauge fixing can be done in many ...
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]
Hole gauge [3] used to gage internal dimensions of bores that are either too small in diameter for an inside micrometer, and have greater economy than a bore gage or other precision internal gage. Caliper: a device used to measure the distance between two opposing sides of an object. Center gauges and fishtail gauges
Quantum electrodynamics is an abelian gauge theory with the symmetry group U(1) and has one gauge field, the electromagnetic four-potential, with the photon being the gauge boson. The Standard Model is a non-abelian gauge theory with the symmetry group U(1) × SU(2) × SU(3) and has a total of twelve gauge bosons: the photon , three weak bosons ...
Gauge block, a metal or ceramic block of precisely known dimension, used in measuring; Sight glass, also known as a water gauge, for measuring liquid level heights in storage tanks and pressure vessels; Boost gauge, a gauge used in conjunction with turbo-super-chargers; Pressure gauge or vacuum gauge, see pressure measurement
A caliper using a calibrated screw for measurement, rather than a slide, is called an external micrometer caliper gauge, a micrometer caliper or, more often, simply a micrometer. (Sometimes the term caliper, referring to any other type in this article, is held in contradistinction to micrometer.)
Consider a generic (possibly non-Abelian) gauge transformation acting on a component field = =.The main examples in field theory have a compact gauge group and we write the symmetry operator as () = where () is an element of the Lie algebra associated with the Lie group of symmetry transformations, and can be expressed in terms of the hermitian generators of the Lie algebra (i.e. up to a ...