相关论文: Manifold Topology, Observables and Gauge Group

I argue that the gauge group of noncommutative gauge theory consists of maps into unitary operators on Hilbert space of the form $u=1+K$ with $K$ compact. Some implications of this proposal are outlined.

Normal elements (or multipliers) of the C* algebra of a certain class of locally compact groupoids admit a natural faithful representation as normal operators on the $L^2$-space of a dense orbit of the groupoid. We prove norm estimates on…

The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition…

We discuss some consequences of the fact that symmetry groups appearing in compactified (super-)gravity may be non-simply connected. The possibility to add fermions to a theory results in a simple criterion to decide whether a 3-dimensional…

Using the equivalence between Scherk-Schwarz reductions and twisted tori compactifications, we discuss the effective theories obtained by this procedure from M-theory and N =4 type II orientifold constructions with Neveu-Schwarz and…

Let $G$ be a second countable locally compact groupoid equipped with a Haar system $\lambda$.In this work, we introduce and develop the notion of amenability for continuous unitary representations of $G$, formulated in terms of Hilbert…

Borchers and Wiesbrock have demonstrated certain results concerning the one-parameter semigroups of endomorphisms of von Neumann algebras that appear as lightlike translations in the theory of algebras of local observables. These results…

We develop a new mathematical approach to diffeomorphism invariant quantum states for the quantisation of general field theories such as general relativity and modified gravity. Treating quantum fields as fibre bundles, we discuss operators…

We establish a correspondence between information geometry and gauge theory. First, we define an important class of statistical manifolds, that is normalized and satisfies a conservation field equation. Second, we prove that for a…

For an $S_4$ space-time manifold global aspects of gauge-fixing are investigated using the relation to Topological Quantum Field Theory on the gauge group. The partition function of this TQFT is shown to compute the regularized Euler…

This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the…

The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…

Let G be a reductive algebraic group over a field of prime characteristic. One can associate to G (or subgroups thereof) its Lie algebra, its Frobenius kernels, and the finite Chevalley group of points over a finite field. The…

We introduce a very natural topology on the set of total orderings of monomials of any algebra having a countable basis over a field. This topological space and some notable subspaces are compact. This topological framework allows us to…

Within the framework of the universal algebra of the electromagnetic field, the impact of globally neutral configurations of external charges on the field is analyzed. External charges are not affected by the field, but they induce…

To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…

A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…

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…

This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…

Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…