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Results tagged with gauge-theory
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user 124549
Gauge theory in physics and mathematics refers to a field theory whose fields include principal bundles with connection.
6
votes
3
answers
678
views
Electromagnetism as a $U(1)$-gauge theory
I would like to learn gauge theory, starting from the simplest case. I have heard that I should start with electromagnetism, which is just the $U(1)$-gauge theory. All the references I know are writte …
- 5,230
5
votes
0
answers
126
views
Uniqueness of Witten-Dijkgraaf 2D TQFT at 0th dimension
If I understand correctly, Dijkgraaf-Witten TQFT in dimension 2 is the
following. Fix any finite group $G$, we define a field over a closed
2-manifold to be a principle $G$ bundle (it's automatically …
- 5,230
6
votes
2
answers
832
views
1-dimensional pure gauge theory
I am learning TQFT from compact Lie groups by Freed, Hopkins, Lurie,
and Teleman: https://arxiv.org/abs/0905.0731 , and got stuck very hard
even in the first section ($n = 1$), which was "trivial but …
- 5,230
4
votes
2
answers
528
views
How much do characteristic classes fail to characterize bundles?
Given a group $G$, let $E \to B$ be a principal $G$-bundle. It is
well-known that when $B$ is a nice enough topological space (e.g.
CW-complex), such a thing corresponds to a connected component of
$H …
- 5,230
9
votes
0
answers
202
views
Donaldson invariants for piecewise-linear $4$-manifolds
It is well known that in dimension $4$, the notion of piecewise linear manifolds and the notion of smooth manifolds are the same [1][2]. On the other hand, the computations of Donaldson invariants inv …
- 5,230