I've always wondered about relating a gauge field in QFT to the connection coefficients in GR. You say the analogue to the curvature in spacetime is a curvature in gauge space, I'm trying to wrap my head around that. How do you interpret different curvatures of gauge space? The size of the gauge orbit or something? Great video!
The curvatures of gauge spaces are the field strength tensors. That's how you interpret them. I have a video on deriving GR like a gauge theory that may add to your understanding some. It's called "The Tetradic Palatini Formulation Of General Relativity." The most satisfying understanding of all of this lies in rather abstract differential geometry, specifically in more generalized connection theory. Unfortunately, I don't think I can give a very complete description of that answer now, but essentially gauge fields are connection fields.
🍎 Color charge propagation speed is √1√2√3=√6 times the speed of the propagation speed of electromagnetic waves. 8π/c^4 of the Einstein equation is 8π/√6^4= 8π/36=(1/4)(8π/9)=(2π/9), and E =mc^2→m√6^2=m6 , Rμν-(1/2)gμνR= 8πG Tμν /c^4= (1/4)(8π/9)G Tμν, // gluon // or (1/4)(8/9)GTμν (π=1, c=1), ･･･❶ E =mc^2 ⇒ m√6^2=m6, // E=m1c^2, E=m2c^2, E=m3c^2, E =m6c^2 // I think the mass gap problem of Yang-Mills theory was solved with E = m6 . Speed of EM light √1c, ･･･❷ propagation speed of 2 color charges √2c, ･･･❸ propagation speed of 3 color charges √3c, ･･･❹ propagation speed of quark lepton √6c, ･･･❺ 達磨さんが転んだ！ 発音の数は10。 Daruma-san has fallen ! The landscape of the QCD Lagrange Density, which has been decomposed into Gluon and Quark Lepton, has five expressions. A macro example of a membrane space is the solar system. The sun's surface activity becomes D-BRANE. Prominence is an open string. Closed strings are released to the six planets by corona, the solar wind. Quarks and leptons correspond to planets, satellites, asteroids, dwarf planets, exoplanets, and interstellar materials.
I've always wondered about relating a gauge field in QFT to the connection coefficients in GR. You say the analogue to the curvature in spacetime is a curvature in gauge space, I'm trying to wrap my head around that. How do you interpret different curvatures of gauge space? The size of the gauge orbit or something? Great video!
The curvatures of gauge spaces are the field strength tensors. That's how you interpret them.
I have a video on deriving GR like a gauge theory that may add to your understanding some. It's called "The Tetradic Palatini Formulation Of General Relativity."
The most satisfying understanding of all of this lies in rather abstract differential geometry, specifically in more generalized connection theory. Unfortunately, I don't think I can give a very complete description of that answer now, but essentially gauge fields are connection fields.
Dietterich Labs I’ll check out your other video, keep up the good work!
Andrew Dotson Lie groups are also differentiable manifolds. GR uses manifolds, QFT uses groups.
@@AndrewDotsonvideos a wild Dotson spotting!
I think you can look at the QFT book by L. H Ryder for such discussions on connection to GR
Where can I download them pdfs?
Very good, honestly just wanted a quick video for a run down of Yang Mills to get the general idea and I have to thank you
great video! please consider doing a video on electroweak unification
dude i love it, this saved my life, keep it up!
I am glad that my video helped!
this is incredibly important content
can you explain where the factor of -1/2 comes from? i cant seem to figure it out.
Holy crap I love this stuff you’re the man
Thanks!
@@DietterichLabs Would you mind sharing the notes? It'd be awesome dude, btw you're a hero 🎉
What do we mean by gauge theory ?
@DietterichLabs Why not U(N) instead of SU(N)?
7 quality physicists in the chat.. figured I'd let ya'll know that I'm currently comparing pulsar spin down rates to solar cycles & it feels so right
please share the reference
Very Well.
🍎
Color charge propagation speed is √1√2√3=√6 times the speed of the propagation speed of electromagnetic waves.
8π/c^4 of the Einstein equation is 8π/√6^4= 8π/36=(1/4)(8π/9)=(2π/9), and
E =mc^2→m√6^2=m6 ,
Rμν-(1/2)gμνR=
8πG Tμν /c^4=
(1/4)(8π/9)G Tμν,
// gluon //
or
(1/4)(8/9)GTμν
(π=1, c=1),
･･･❶
E =mc^2
⇒
m√6^2=m6,
// E=m1c^2, E=m2c^2, E=m3c^2, E =m6c^2 //
I think the mass gap problem of Yang-Mills theory was solved with E = m6 .
Speed of EM light √1c, ･･･❷
propagation speed of 2 color charges √2c, ･･･❸
propagation speed of 3 color charges √3c, ･･･❹
propagation speed of quark lepton √6c, ･･･❺
達磨さんが転んだ！
発音の数は10。
Daruma-san has fallen !
The landscape of the QCD Lagrange Density, which has been decomposed into Gluon and Quark Lepton, has five expressions.
A macro example of a membrane space is the solar system. The sun's surface activity becomes D-BRANE. Prominence is an open string. Closed strings are released to the six planets by corona, the solar wind. Quarks and leptons correspond to planets, satellites, asteroids, dwarf planets, exoplanets, and interstellar materials.
#likes/#dislikes = infinite
I hope no one figures out how to renormalize that divergence!
@@DietterichLabs Hehehehe....we don't want to see that solution now, do we?
I have a degree in Physics and you lost me
It's very small the size of information, sorry this is no good!
poor sciency babies utter big sciency words!