相关论文: Integration on the space of Connections Modulo Gau…
In this article we summarize and describe the recently found transforms for theories of connections modulo gauge transformations associated with compact gauge groups. Specifically, we put into a coherent picture the so-called loop…
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
We analyze the role played by local translational symmetry in the context of gauge theories of fundamental interactions. Translational connections and fields are introduced, with special attention being paid to their universal coupling to…
We give a modern account of the construction and structure of the space of generalized connections, an extension of the space of connections that plays a central role in loop quantum gravity.
Some mathematical aspects of using the translation group as an internal symmetry group in a gauge field theory are presented and discussed. The traditional manner in which gravitation can be accounted for by the introduction of a global…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what…
In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and…
In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge…
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be…
In this talk I shall try to give an elementary introduction to certain areas of mathematical physics where the idea of moduli space is used to help solve problems or to further our understanding. In the wide area of gauge theory, I shall…
A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar…
Let P be a principal bundle with semisimple compact simply connected structure group G over a compact simply connected four-manifold M. In this note we give explicit formulas for the rational homotopy groups and cohomology algebra of the…
In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations of usual symmetries like the external…
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…
Gauge theories of conformal spacetime symmetries are presented which merge features of Yang-Mills theory and general relativity in a new way. The models are local but nonpolynomial in the gauge fields, with a nonpolynomial structure that…
The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall…
We consider the notion of a connection on a principal bundle $P(M,G)$ from the point of view of the action of the tangential group $TG$. This leads to a new definition of a connection and allows to interpret gauge transformations as effect…
In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is…
We give a description of the category structure of the space of generalized connections, an extension of the space of connections that plays a central role in loop quantum gravity.