advanced_tools:gerbes
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advanced_tools:gerbes [2017/11/07 14:41] 162.158.91.86 [Layman] |
advanced_tools:gerbes [2018/05/03 11:42] (current) paul [Intuitive] |
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| ====== Gerbes ====== | ====== Gerbes ====== | ||
| - | <tabbox Why is it interesting?> | ||
| - | <blockquote>Gerbes show up when we try to invent a kind of "higher gauge theory" that describes how not just point particles but 1-dimensional objects transform when you move them around. For example, the strings in string theory, or the loops in loop quantum gravity.<cite>http://www.math.ucr.edu/home/baez/week210.html</cite></blockquote> | ||
| - | <tabbox Layman> | + | <tabbox Intuitive> |
| <blockquote>If the Guardian asked me to explain a gerbe, I’d cheat a little and explain a gerbe with connection, which is actually easier. I’d say it’s a well-behaved recipe that’ll tell you a time of day — by giving a position of a clock hand — if you specify a way of sticking a balloon in a given space. The rules for what counts as “well-behaved” would take a few pictures to explain, but the first rule is that as you move the balloon around in a smooth sort of way, the time of day changes in a smooth sort of way.<cite>[[https://golem.ph.utexas.edu/category/2007/08/gerbes_in_the_guardian.html|John Baez]]</cite></blockquote> | <blockquote>If the Guardian asked me to explain a gerbe, I’d cheat a little and explain a gerbe with connection, which is actually easier. I’d say it’s a well-behaved recipe that’ll tell you a time of day — by giving a position of a clock hand — if you specify a way of sticking a balloon in a given space. The rules for what counts as “well-behaved” would take a few pictures to explain, but the first rule is that as you move the balloon around in a smooth sort of way, the time of day changes in a smooth sort of way.<cite>[[https://golem.ph.utexas.edu/category/2007/08/gerbes_in_the_guardian.html|John Baez]]</cite></blockquote> | ||
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| - 2) paint all the handrails | - 2) paint all the handrails | ||
| - | -3) paint all the walls. | + | - 3) paint all the walls. |
| But it tuns out that the architect used lots of different materials all over the place. You find that you need different amounts of paint to color these items at different places. | But it tuns out that the architect used lots of different materials all over the place. You find that you need different amounts of paint to color these items at different places. | ||
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| - a gerbe with connection.<cite>[[https://golem.ph.utexas.edu/category/2007/08/gerbes_in_the_guardian.html|Urs Schreiber]]</cite></blockquote> | - a gerbe with connection.<cite>[[https://golem.ph.utexas.edu/category/2007/08/gerbes_in_the_guardian.html|Urs Schreiber]]</cite></blockquote> | ||
| - | <tabbox Student> | + | <tabbox Concrete> |
| <note tip>Gerbes are generalization of principal [[advanced_tools:fiber_bundles|bundles]].</note> | <note tip>Gerbes are generalization of principal [[advanced_tools:fiber_bundles|bundles]].</note> | ||
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| * [[http://www.ams.org/notices/200302/what-is.pdf|What is a Gerbe?]] by Nigel Hitchin; see also the comment about it [[https://www.theguardian.com/education/2007/aug/21/highereducation.research|here]] and the discussion [[https://golem.ph.utexas.edu/category/2007/08/gerbes_in_the_guardian.html|here]]. | * [[http://www.ams.org/notices/200302/what-is.pdf|What is a Gerbe?]] by Nigel Hitchin; see also the comment about it [[https://www.theguardian.com/education/2007/aug/21/highereducation.research|here]] and the discussion [[https://golem.ph.utexas.edu/category/2007/08/gerbes_in_the_guardian.html|here]]. | ||
| - | <tabbox Researcher> | + | <tabbox Abstract> |
| <note tip> | <note tip> | ||
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| - | <tabbox Examples> | + | <tabbox Why is it interesting?> |
| + | <blockquote>Gerbes show up when we try to invent a kind of "higher gauge theory" that describes how not just point particles but 1-dimensional objects transform when you move them around. For example, the strings in string theory, or the loops in loop quantum gravity.<cite>http://www.math.ucr.edu/home/baez/week210.html</cite></blockquote> | ||
| - | --> Example1# | ||
| - | + | <blockquote>The Euler-Lagrange p-gerbes [...] are singled out as being exactly the right coherent refinement | |
| - | <-- | + | of locally defined local Lagrangians that may be integrated over a (p+1)-dimensional spacetime/worldvolume |
| - | + | to produce a function, the action functional.<cite>https://arxiv.org/abs/1601.05956</cite></blockquote> | |
| - | --> Example2:# | + | |
| - | + | ||
| - | + | ||
| - | <-- | + | |
| - | + | ||
| - | <tabbox FAQ> | + | |
| - | + | ||
| - | <tabbox History> | + | |
| </tabbox> | </tabbox> | ||
advanced_tools/gerbes.1510062086.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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