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Gauge Structure (or Gauge Symmetry)
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Historical Context and Formal Development
The concept originated in the early 1920s through the work of Hermann Weyl, who initially proposed a global scale invariance (or "gauge theory" (global)) to link electromagnetism with gravitation, suggesting that the length of spacetime vectors should be locally scalable without altering the physics. This initial formulation proved physically untenable, as it implied that fundamental atomic spectral lines would shift depending on the traject… -
Gauge Symmetry
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Weyl's gauge theory faced immediate difficulties, primarily because it violated the conservation of mass in physical interactions, leading to contradictions with experimental observations of spectral lines. The key difficulty was that the transformation was conformal (dependent on position $x^\mu$), affecting both length and time intervals inconsistently.
The theory was rescued in the 1920s when Vladimir Fock and Fritz London independently realized that replacing the geometric length scaling with a *phase… -
Gauge Theory
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The initial motivation for gauge invariance arose in classical electromagnetism through the work of Hermann von Helmholtz in the 1870s, long before its modern quantum mechanical formulation. Helmholtz sought a description of electrodynamics where the physics was independent of the choice of scalar potential ($\phi$) and vector potential ($\mathbf{…