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Graph, Wall, Tome: Difference between revisions
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* Also in (ii), “nonabelian gauge group G” should be changed to nonabelian structure group G. | * Also in (ii), “nonabelian gauge group G” should be changed to nonabelian structure group G. | ||
* In (iii), R and R should be (complex) linear representations of G and so they are not equivalent. | * In (iii), R and R should be (complex) linear representations of G and so they are not equivalent. | ||
== The Wall == | |||
[[File:The-wall.png]] | |||
[http://www.math.stonybrook.edu/~tony/scgp/wall-story/wall-story.html Source] | |||
Eric talked about some of the important equations on the wall. There are 2 different recorded versions of the conversation if you want to listen to it. | |||
== The Tome == | |||
[https://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311 Road to Reality by Roger Penrose (2004)] | |||
ISBN: 978-0679776314 | |||
== Questions == | |||
Some questions Eric posed related to the assignment: | |||
=== What is FA geometrically? === | |||
[https://en.wikipedia.org/wiki/Atiyah%E2%80%93Singer_index_theorem Atiyah-Singer index theorem] | |||
=== What is R and R geometrically? === | |||
[https://en.wikipedia.org/wiki/Einstein_field_equations Einstein field equaitions] | |||
Einstein’s original publication, Die Feldgleichungen der Gravitation, in English | |||
=== How do they relate? === | |||
[https://en.wikipedia.org/wiki/Cohomology Cohomologhy] | |||
=== What does this have to do with Penrose Steps? === | |||
* [https://en.wikipedia.org/wiki/Penrose_stairs Penrose stairs] | |||
* [https://en.wikipedia.org/wiki/Spino Spino] | |||
We’ve heard Eric talk about Penrose stairs and spinors - essentially phenomena where you cannot return to the original state through a 360 degree rotation, but require a 720 degree rotation. | |||
=== What are “Horizontal Subspaces” and what do they have to do with Vector Potentials or Gauge fields? === | |||
* [https://en.wikipedia.org/wiki/Vertical_and_horizontal_bundles Vertical and horizontal bundles] | |||
* [https://en.wikipedia.org/wiki/Introduction_to_gauge_theory Introduction to gauge theory] | |||
* [https://en.wikipedia.org/wiki/Symmetry_(physics) Symmetry] | |||
From '''theplebistocrat''': | |||
<blockquote>Generally, we're wanting to understand how fermions arise from - or are embedded within / upon - topological "spaces" that have distinct rules which govern operations within those topological spaces, and then how those rules produce higher dimensional operations in corresponding spaces. | |||
Just intuitively, and geometrically speaking, the image that I'm getting when describing all of this and trying to hold it in my head is the image of a sort of Penrose Tower of Babel, where the fundamental underlying structures reach upwards (but also downwards and inwards?) before reaching a critical rotation that corresponds to a collapse of structure into a higher dimensional fiber bundle. | |||
But doesn't this require the symmetry break? How is left and right rotation in a subspace transformed into verticality? This is a crazy rabbit hole, friends. Keep your chins up. Let me know if this was helpful or leading astray. | |||
</blockquote> | |||