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If is a subset of a real or complex vector space, then the Minkowski functional or gauge of is defined to be the function: [,], valued in the extended real numbers, defined by ():= {: >}, where the infimum of the empty set is defined to be positive infinity (which is not a real number so that () would then not be real-valued).
QED is generally regarded as the first, and simplest, physical gauge theory. The set of possible gauge transformations of the entire configuration of a given gauge theory also forms a group, the gauge group of the theory. An element of the gauge group can be parameterized by a smoothly varying function from the points of spacetime to the ...
For the leptons, the gauge group can be written SU(2) l × U(1) L × U(1) R. The two U(1) factors can be combined into U(1) Y × U(1) l, where l is the lepton number. Gauging of the lepton number is ruled out by experiment, leaving only the possible gauge group SU(2) L × U(1) Y. A similar argument in the quark sector also gives the same result ...
the gauge as used in the definition of the Henstock-Kurzweil integral, also known as the gauge integral; in fractal geometry, a synonym for dimension function; in control theory and dynamical systems, a synonym for Lyapunov candidate function; in gauge theory, a synonym for gauge symmetry. a type of Minkowski functional
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 "lamp looks weird" trend originated from an old Reddit post by an anonymous user who experienced a lifetime of memories in a span of a few moments after sustaining a head injury.. In the story ...
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 ...
The Philadelphia Eagles have been one of the NFL’s hottest teams. Bettors know all about it. The Eagles have won eight in a row since their bye and they’ve been nearly as good against the spread.