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Final Answers
© 2000-2023 Gérard P. Michon, Ph.D.

Gauge Theories

 Joseph-Louis Lagrange  
 1736-1813  Jean-le-Rond d'Alembert 
 1717-1783  Pierre-Louis Moreau de Maupertuis 
 1698-1759  Isaac Newton  
 1643-1727  Pierre de Fermat 
 1601-1665  

Related articles on this site:

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Related Links (Outside this Site)

Gauge Principle for Ideal Fluids & Variational Principle  by  Tsutomu Kambe
What is a Gauge?  by  Terry Tao  (What's new, 2008-09-27).
Hopf bundle (1931) by  Heinz Hopf (1894-1971)   |   Planet Hopf (0:15).
Seiberg-Witten theory (1:22:11, 2:06:03)  by  Ed Witten  (IAS, 2017-07-10).
Masses, Mixings and Yukawa Couplings  by  Arcadi Santamaria  (Feb. 1993).

Wikipedia :   Gauge fixing   |   Gauge covariant derivative   |   Covariant derivative   |   Fiber bundle

Videos :   Quantum Invariance (13:03)  by  Matt O'Dowd  (2018-07-11).
Classical Field Theory  by  Leonard Susskind1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
Quarks & the Magic of Gauge Theory (12:35)  by  Murray Gell-Mann   (2011).
Biggest Idea #15:  Gauge Theory (1:17:57)  by  Sean M. Carroll  (2020-04-21).
:Gauge symmetriies (37:38)  Elliot Schneider  (Physics with Elliot, 2022-04-14).

 
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Gauge Theory

In Gauge Theory,  it turns out,  the  symmetries  determine the dynamics.
Murray Gell-Mann  (1929-2019) 

(2009-07-21)     Fluid Mechanics  &  Material Derivative
Tracking actual particles in a fluid.

 Come back later, we're
 still working on this one...


(2018-07-31)   Gauge invariance  of electrodynamics  (L. Lorenz, 1867)
Maxwell was aware of gauge symmetries from the very beginning (1864).

To justify the  famous equations  he devised in 1864,  James Clerk Maxwell proposed all-but-forgotten  mechanaical analogies  which did imply  gauge symmetries  similar to those which can be encountered in  fluid mechanics,  although he never stressed that point.

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 still working on this one...


(2023-02-25)     Yukawa intercation via particle mediation.
Invented for the strong force, revived for the Higgs scalar boson  (spin 0).

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 still working on this one...

Yukawa interaction (1935)   |   Hideki Yukawa (1907-1981, Nobel 1949)


(2023-02-21)     Klein-Gordon Equation
Massive bosons mediate fields of limited range.

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 still working on this one...


(2023-02-21)     Scalar Electrodynamics
Putting the Klein-Gordon theory together with electromagnetism.

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 still working on this one...


(2023-02-21)     Quantum Electrodynamics
Electron spinor field  Y  and electromagnetic field  Am .

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 still working on this one...

Covariant Potential and the Faraday Tensor

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