Stacks [The Physics Travel Guide]

--- advanced_tools:stacks [2017/11/08 18:04]
jakobadmin [Researcher]
+++ advanced_tools:stacks [2017/11/09 09:52] (current)
jakobadmin [History]
@@ Line 9: / Line 9: @@
 by Grothendieck in the second half of the 20th century and as
 witnessed by a multitude of modern developments, a more natural mathematical
-description of many phenomena in geometry is obtained by re-
+description of many phenomena in geometry is obtained by refining from traditional geometric spaces to more refined kinds of spaces
-fining from traditional geometric spaces to more refined kinds of spaces
 known as “stacks”.
+[...]
+Our main motivation to consider sheaves and stacks is to provide a nonperturbative
+framework in which we can do physics. Much of gauge theory is
+done in perturbation theory, but in fact **non-perturbative effects** such as Dirac
+monopoles and Yang-Mills instantons play a crucial role in fundamental physics
+[5]. **The language of stacks is the natural language for these phenomena.**
 <cite>https://ncatlab.org/schreiber/files/Eggertsson2014.pdf</cite></blockquote>
@@ Line 47: / Line 55: @@
 <tabbox History>
+The idea of using stacks goes back to a manuscript titled Pursuing Stacks by Alexander Grothendieck in 1983. For some more information, see https://ncatlab.org/nlab/show/Pursuing+Stacks
 </tabbox>