# Why are gauge theories called so?

Why are gauge theories called so? I guessed it was because gauge also means to estimate, so when one is trying to find the gauge theory for such and such interactions one has to estimate what might be the best gauge group for that interaction. Does this make sense?

• In a book I have written by Leonard Susskind he says: It is called a gauge transformation. Why "gauge"? Its a historical glitch. At one time it was wrongly thought to reflect ambiguities in gauging lengths at different locations. Oct 11 '16 at 18:31
• Would History of Science and Mathematics be a better home for this question? Oct 11 '16 at 18:37
• @Qmechanic That's the same question I asked myself. I'm not sure, though. Oct 11 '16 at 18:41
• I'm voting to close this question as off-topic because it is about history, not science, and should be on history of science and mathematics. Oct 11 '16 at 21:28

Thus, the first gauge group was $\mathbb{R}^+$ of positive reals under multiplication, in late 1920s Weyl went from a field of gauges to a field of phases, replacing $\mathbb{R}^+$ with $U(1)$, but the name stuck. In this new theory Weyl was able to give a gauge theoretic explanation of the conservation of electric charge. Dirac replaced the $U(1)$ fields with the sections of associated complex line bundles in 1931, and noticed the possibility of magnetic monopoles when the bundles were globally non-trivial. Non-Abelian gauge theories did not appear until Yang and Mills in 1950s.
• @WetSavannaAnimalakaRodVance Yes, and Eich is calibration/gauge/scale in German. But modern gauge theories are closer in spirit to the $U(1)$ version, so it should really be phase theory, phase fixing and phase invariance :) Oct 14 '16 at 0:49