Michael Rios & David Chester - Conversations with Scientists: Lie Algebras and Extremal Black Holes

Like and subscribe. This is an archive channel, i'm not the owner of the content, check the link in the end. Mathematicians & QGR Friends Michael Rios & David Chester walk around UCLA and discuss mathematics and physics.

The study of particle physics relies on Lie algebras for Yang-Mills theories, such as the standard model. Gravity, on the other hand, is described by Riemannian geometry that doesn't include the needed "unitary" Lie algebras used to describe standard model matter and force particles. Quarks and their corresponding force particles, the gluons, are described by the Lie algebra SU(3). In order to combine, this SU(3) "color" symmetry with Einstein's gravity, a mathematical object called a fiber bundle can be used.

Moreover, since the 1960's a more advanced form of the fiber bundle was envisioned by mathematician Alexander Grothendieck, and this is now known as non-commutative geometry. The physics of extended objects in string theory that generalize the string, called "D-branes", were found to inherently exist in non-commutative geometries. Mike and David agree that many of the hints of a "unified theory" are already published and need to be pieced together like a puzzle.

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