All Questions
Tagged with gauge-theory fa.functional-analysis
7 questions
0
votes
1
answer
143
views
Gauge invariance issues of YM theories in 2D Euclidean space
In order to be clear, I will write down every component explicitly. Also, I assume Euclidean metric in this post, so that spacetime indices are written as $i,j$ rather than $\mu, \nu$.
Following Wiki, ...
- 6,696
0
votes
0
answers
246
views
Finding a unitary operator on L^{2}(\mathbb{R}^{2},dxdy)
I have a one parameter (r) family of self-adjoint representations of the universal enveloping algebra of some nilpotent Lie group on $L^{2}(\mathbb{R}^{2},dxdy)$ as follows:
$$\hat{X}^{r}=\hat{x}-i(r-...
- 103
2
votes
0
answers
196
views
Gauge invariance of a QFT path integral
If we consider the usual formal construction of a path integral over fields with gauge symmetries e.g as in Weinbergs "The Quantum Theory of Fields - Volume 2" the notion of gauge invariance ...
- 651
4
votes
1
answer
229
views
Orientability of moduli space and determinant bundle of ASD operator
Setting
In instanton gauge theory, given a $G$-principal bundle $P\to X^4$, the orientability of the moduli space of ASD connections
$$\mathcal{M}_k = \{A \in L^{2}_{k}(X, \Lambda^1 \otimes\mathrm{...
- 2,533
13
votes
0
answers
372
views
Finite dimensional approximation of Donaldson theory
In addition to the Seiberg-Witten invariant there has been further success with "finite dimensional approximations" of the Seiberg-Witten theory: Bauer-Furuta's stable (co)homotopy invariants, and ...
- 17.5k
2
votes
2
answers
981
views
Elliptic operator becomes Fredholm
Let $X$ be a Riemannian $n$-manifold with tubular end $\mathbb R^+\times Y$, where $Y$ is a closed $n-1$-manifold. Suppose $L:L^{p,w}_2(X)\to L^{p,w}(X)$ is the Laplacian operator which is ...
- 376
12
votes
0
answers
478
views
What is known about the Yang-Mills stratification over 3-manifolds?
Rade proved in his thesis (Crelle's Journal, 1992, available here: digizeitschriften.de/dms/toc/?PPN=PPN243919689) that if $E\rightarrow M$ is a $U(n)$-bundle over a 3-manifold, then the gradient flow ...
- 8,803