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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.
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 Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 for its solution. The problem is phrased as follows: [1] Yang–Mills Existence and Mass Gap.
This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson.
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.
The Coulomb gauge (also known as the transverse gauge) is used in quantum chemistry and condensed matter physics and is defined by the gauge condition (more precisely, gauge fixing condition) (,) =. It is particularly useful for "semi-classical" calculations in quantum mechanics, in which the vector potential is quantized but the Coulomb ...
Positivity of the measure and gauge invariance are sufficient to prove the theorem. [7] This is also an explanation for why gauge symmetries are mere redundancies in lattice field theories, where the equations of motion need not define a well-posed problem as they do not need to be solved. Instead, Elitzur's theorem shows that any observable ...
The Wess–Zumino gauge (a prescription for supersymmetric gauge fixing) provides a successful solution to this problem. Once such suitable gauge is obtained, the dynamics of the SUSY gauge theory work as follows: we seek a Lagrangian that is invariant under the Super-gauge transformations (these transformations are an important tool needed to ...