All Questions
Tagged with gauge-theory reference-request
24 questions
2
votes
0
answers
74
views
Is it likely that gradient flow trajectories of a $G$-invariant function pass through degenerate points?
This question may be posed somewhat vaguely, but I'm interested to actually get an idea of what to expect, so I try to not target it at a specific result.
Assume that $G$ is a compact Lie group, ...
- 139
0
votes
0
answers
117
views
An interesting identity involving skew-Schur functions
Denote $\rho=(-\frac12,-\frac32,-\frac52,\dots)$. I was reading this interesting paper, where in particular, the authors claim that one can get the expression in (2.9)
\begin{align*}
\prod_{k\geq1}(1+...
- 43.2k
7
votes
1
answer
880
views
Is there a program to solve The Yang–Mills Existence and Mass Gap problem similar to the Hamilton's program to solve Poincaré Conjecture?
According to Wikipedia:
"Hamilton's program was started in his 1982 paper in which he introduced the Ricci flow on a manifold and showed how to use it to prove some special cases of the Poincaré ...
user483779
6
votes
3
answers
716
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 ...
- 5,230
12
votes
1
answer
680
views
Reference request: Gauge natural bundles, and calculus of variation via the equivariant bundle approach
Let $P\rightarrow M$ be a principal fibre bundle with structure group $G$, $F$ a manifold and $\alpha: G\times F\rightarrow F$ a smooth left action.
There is an associated fibre bundle $E\rightarrow ...
- 2,792
3
votes
0
answers
309
views
Gauge structure of teleparallel gravity
I am interested in references that treat teleparallel gravity in a mathematically rigorous manner, especially in regards to it being a "gauge theory of the translation group".
The standard reference ...
- 2,792
1
vote
1
answer
840
views
Reference request: Gauge theory [closed]
What are some good introductory texts to gauge theory? I have some basic differential geometry knowledge, but I don’t know any algebraic geometry.
Also, as a side question, what intuitively is a ...
- 2,069
2
votes
0
answers
239
views
Reference Request: A "Chevalley-Eilenberg"-style formulation of the $L_\infty$ algebra minimal model theorem?
The nicest definition of $L_\infty$-algebras ---which I will call a "Chevalley-Eilenberg" style definition after the obvious analogy with the Chevalley-Eilenberg differential of Lie algebras--- is the ...
- 784
8
votes
0
answers
251
views
Exact triangle for monopole Floer homology with $\mathbb{Z}$-coefficient
Let $Y$ be oriented 3 manifold with torus boundary and let $\gamma_{j}$ (j=0,1,2) be three curves on its boundary with $\#(\gamma_{j}\cap \gamma_{j+1})=-1$. We denote by $Y_{j}$ the manifold obtained ...
- 1,069
3
votes
1
answer
333
views
Elementary question: Curvature change under Complexified Gauge Transformation
Forgive me for this elementary question.
Let $E$ be a holomorphic vector bundle over a Riemann surface $M$ equipped with a Hermitian metric. Let $\nabla$ be the compatible connection on $E$ amd $g$ ...
- 297
1
vote
1
answer
1k
views
Mathematics Book on Yang-Mills Equation [duplicate]
I am planning to read two papers - Atiyah-Bott's paper on Yang-Mills equations on Riemann surfaces and Hitchin's Self-Duality equations on Riemann Surface. Can someone please suggest some book where ...
- 789
4
votes
2
answers
1k
views
Local structure of the quotient of a Lie group action
Suppose $M$ is a smooth manifold and a compact Lie group $G$ acts freely on $M$, then it is well known that $M/G$ has a manifold structure.
Are there any results for the general case? (a) If the ...
- 957
9
votes
2
answers
1k
views
What is the BRST-anti-BRST formalism?
What is the BRST-anti-BRST formalism?
Is the Sp(2) doublet the ghost, antighost pair?
Introductory accounts of this subject seem to be hard to find. I would appreciate a reference for someone who ...
- 3,880
4
votes
2
answers
1k
views
Gauge-theoretic formulation of Maxwell equations [duplicate]
Does any one know how to write the Maxwell equations as an equation on a principal $U(1)$-bundle?
In Freed & Uhlenbeck's Instantons and Four manifolds, the authors claim that the Maxwell ...
- 957
9
votes
3
answers
751
views
What is the definition of picture changing operation?
What is the definition of picture changing operation?
What is a standard reference where it is defined - not just used?
- 3,880
3
votes
0
answers
1k
views
A gentle introduction to CFT [closed]
1) Which is the definition of a conformal field theory?
2) Which are the physical prerequisites one would need to start studying conformal field theories?
(i.e Does one need to know supersymmetry? ...
- 489
5
votes
1
answer
261
views
Conjecture on homotopy groups of moduli space of self-dual connections
In the paper Stability in Yang-Mills Theories (1983), Taubes puts a (topological) bound on the Hessian of the YM-action on $S^4$. He consequently conjectured:
"The inclusion $\mathcal{M}_n\...
- 17.5k
8
votes
1
answer
2k
views
Relation of SW and Donaldson Invariant
My question is:
I am request for the reference that Is there any relationship between the Seiberg-Witten Invariant and Donaldson's Invariant? Or the relationship between Seiberg-Witten Moduli Space ...
- 703
1
vote
1
answer
391
views
Reference request: Seminal papers in gauge-theoretic mathematics [closed]
Following on from previous question I was also searching for seminal papers in gauge theory.
Would be greatly appreciative of references to such.
- 279
5
votes
2
answers
739
views
Reference request: Introductions to current mathematics derived from / related to gauge theories
I was searching for introductions to current mathematics related to gauge theories.
Can someone suggest some good references?
E.g.
Topics in Physical Mathematics by K. Marathe
- 279
6
votes
0
answers
437
views
Has anyone seen this Hitchin-like system?
Let $(M,g)$ be a riemannian manifold and let $P\to M$ be a principal $G$-bundle with connection $A$. Let $\alpha \in \Omega^1(M;\mathrm{ad}P)$ be a one-form on $M$ with values in the adjoint bundle $\...
- 33.3k
8
votes
1
answer
2k
views
K.Uhlenbeck's preprint "A priori estimates for Yang-Mills fields"
Does anyone have a copy of the unpublished preprint of Karen Uhlenbeck A priori estimates for Yang-Mills fields from around 1986?
It appears to have circulated for some time, and it is quoted in ...
- 6,871
33
votes
4
answers
3k
views
What is the precise statement of the correspondence between stable Higgs bundles on a Riemann surface, solutions to Hitchin's self-duality equations on the Riemann surface, and representations of the fundamental group of the Riemann surface?
I am trying to find the precise statement of the correspondence between stable Higgs bundles on a Riemann surface $\Sigma$, (irreducible) solutions to Hitchin's self-duality equations on $\Sigma$, and ...
- 21k
11
votes
3
answers
3k
views
Looking for reference on gauge fields as connections.
Can anyone give me references where I would see a detailed exposition of how to translate gauge field theory as known to physicists into the language of connections. I am looking for a detailed ...
- 3,541