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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 Intuitive> | |
- | <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> | + | |
- | <tabbox Layman> | + | |
<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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- 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> | ||