相关论文: Gauge Orbit Types for Generalized Connections
The action of Ashtekar's generalized gauge group $\Gb$ on the space $\Ab$ of generalized connections is investigated for compact structure groups $\LG$. First a stratum is defined to be the set of all connections of one and the same gauge…
The properties of the space $\A$ of regular connections as a subset of the space $\Ab$ of generalized connections in the Ashtekar framework are studied. For every choice of compact structure group and smoothness category for the paths it is…
We prove a myriad of results related to the stabilizer in an algebraic group $G$ of a generic vector in a representation $V$ of $G$ over an algebraically closed field $k$. Our results are on the level of group schemes, which carries more…
A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in space-time dimension d<=4 is presented. The method is based on the…
We consider faithful actions of simple algebraic groups on self-dual irreducible modules, and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the…
We give a new description of Rosenthal's generalized homotopy fixed point spaces as homotopy limits over the orbit category. This is achieved using a simple categorical model for classifying spaces with respect to families of subgroups.
Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its closure,…
The bundle structure of the space $\Ab$ of Ashtekar's generalized connections is investigated in the compact case. It is proven that every stratum is a locally trivial fibre bundle. The only stratum being a principal fibre bundle is the…
This is the second of two papers treating faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties; in the first paper we considered the module itself and its projective space, while…
First, we review the basic mathematical structures and results concerning the gauge orbit space stratification. This includes general properties of the gauge group action, fibre bundle structures induced by this action, basic properties of…
In this work, we will introduce the notion of generalized topological groups using generalized topological structure and generalized continuity defined by ?A. Cs?asz?ar [2]. We will discuss some basic properties of this kind of structures…
We determine the orbit types of the action of the group of local gauge transformations on the space of connections in a principal bundle with structure group O(n), SO(n) or $Sp(n)$ over a closed, simply connected manifold of dimension 4.…
Given a base manifold $M$ and a Lie group $G$, we define $\bar{\cal A}^H_M$ a space of generalized $G$-connections on $M$ with the following properties: - The space of smooth connections ${\cal A}^\infty_M = \sqcup_\pi {\cal A}^\infty_\pi$…
The quantum completion of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes an analogous…
The quantum completion of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes the analogous…
Properties of the space $\Ab$ of generalized connections in the Ashtekar framework are investigated. First a construction method for new connections is given. The new parallel transports differ from the original ones only along paths that…
In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception (only in…
We extend the notion of connection in order to be able to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of connection. Using connections,…
For a principal $\rmSU(n)$-bundle over a compact manifold of dimension $2,3,4$, we determine the orbit types of the action of the gauge group on the space of connections modulo pointed local gauge transformations. We find that they are…
We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of…