相关论文: Ehreshmann theory of connection in a principal bun…

We introduce a quantum generalisation of the notion of coupling in probability theory. Several interesting examples and basic properties of quantum couplings are presented. In particular, we prove a quantum extension of Strassen theorem for…

This is the second of three papers I will present as an application of the Basic Unit System concept, a complex mathematical unit presented in The Basic Unit System concept and The Principle of Synergy. In this case this Bus concept is used…

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…

We give an algebro-geometric construction of the Hitchin connection, valid also in positive characteristic (with a few exceptions). A key ingredient is a substitute for the Narasimhan-Atiyah-Bott K\"ahler form that realizes the Chern class…

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…

Transports along path in fibre bundles are axiomatically introduced. Their general functional form and some their simple properties are investigated. The relationships of the transports along paths and lifting of paths are studied.

Our goal in this paper and two sequels is to apply the Yamagami-Muhly-Williams equivalence theorem for Fell bundles over groupoids to recover and extend all known imprimitivity theorems involving groups. Here we extend Raeburn's symmetric…

We summarise the main results that follow from our theory of frequency- and time-resolved photon correlations, which provides exact computations in nontrivial systems. We illustrate the theory with original results as interesting cases can…

I summarize here the logic that leads us to a program for the Theory of the Total Field in Einstein's sense. The purpose is to show that this theory is a logical culmination of the developments of (fundamental) physical concepts and, hence,…

We make evident a curvature tensor for every vector sub-bundle of an arbitrary manifold tangent bundle which reduces to the curvature tensor of an Ehresmann connection in the case of the horizontal sub-bundle of the tangent bundle to the…

For analyzing stationary Yang-Mills connections in higher dimensions, one has to work with Morrey-Sobolev bundles and connections. The transition maps for a Morrey-Sobolev principal $G$-bundles are not continuous and thus the usual notion…

We address the recently introduced notions of generalized principal bundle and generalized principal connection by keeping track of global geometric properties through local coordinate transformation laws. This approach leads us to…

We examine whether the Teleparallel Equivalent of General Relativity (TEGR) can be formulated as a gauge theory in the language of connections on principal bundles. We argue in favor of using either the affine bundle with the Poincar\'e…

By studying the geometric properties of correlation functions on the theory space, we are naturally led to a connection for the infinite dimensional vector bundle of composite fields over the theory space. We show how the short distance…

The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.

Geometric structures on manifolds became popular when Thurston used them in his work on the geometrization conjecture. They were studied by many people and they play an important role in higher Teichm\"uller theory. Geometric structures on…

The parallel linear transports defined by flat linear connection are axiomatically described. On this basis a number of properties, some of which are new, of these transports and connections are derived.

The aim of this article is to proof a necessary and sufficient condition for the existence of a Cartan connection on a principal bundle. After collecting the essentially well known facts to fix the terminology, soldering forms and…

The purpose of this paper is to sketch an approach towards a reconciliation of quantum theory with relativity theory. It will actually be argued that these two theories ultimately rely on one another. A general operator-algebraic framework…

The goal of this paper is to give a short review of recent results of the authors concerning classical Hamiltonian many particle systems. We hope that these results support the new possible formulation of Boltzmann's ergodicity hypothesis…