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

The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional…

We investigate principal bundles over a root stack. In case of dimension one, we generalize the criterion of Weil and Atiyah for a principal bundle to have an algebraic connection.

This work revisits, from a geometric perspective, the notion of discrete connection on a principal bundle, introduced by M. Leok, J. Marsden and A. Weinstein. It provides precise definitions of discrete connection, discrete connection form…

The purpose of this sophomore-level textbook is twofold: to introduce the student to classical electrodynamics and, at the same time, explain in simple terms the quantum theory of conducting substances (in particular, the solid ones). The…

Recently twisted K-theory has received much attention due to its applications in string theory and the announced result by Freed, Hopkins and Telemann relating the twisted equivariant K-theory of a compact Lie group to its Verlinde algebra.…

This is the first of a series of papers that we intend to publish about the epistemology of fundamental physics in its current state. One of the main objectives of these papers is to improve our understanding of fundamental physics (and…

In this work, generalized principal bundles modelled by Lie group bundle actions are investigated. In particular, the definition of equivariant connections in these bundles, associated to Lie group bundle connections, is provided, together…

This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.

The first and shorter part of this thesis deals with the structural assumption of invertibility in a Lie groupoid. When this assumption is dropped, we obtain the notion of a Lie category: a small category, endowed with a compatible…

These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.

We develop a theory of smooth relative connections over the real path algebra $\mathbb{R}Q$ on smooth twisted quiver bundles. We give obstructions to the existence of a smooth relative connection on twisted quiver bundles. For tree-type…

As true as it is that a bricklayer needs a plumb line and a T-square, so it is that a physicist using general relativity needs how to draw geodesics and use fields of congruent vector frames of reference. While the first part of the…

We shall here consider extended theories of gravitation in the metric-affine formalism with matter coupled directly to the connection. A sufficiently general procedure will be exhibited to solve the resulting field equation associated to…

This paper introduces a homology theory for links in I-bundles over an orientable surface. The theory is unique in that the elements of the chain groups are surfaces instead of diagrams. It is then shown this theory yields the same results…

A first step towards a systematic theory of relative line bundles over SUSY-curves is presented. In this paper we deal with the case of relative line bundles over families of ordinary Riemann surfaces. Generalizations of the Gauss-Bonnet…

We introduce a notion of a connection on a coherent sheaf on a weighted projective line (in the sense of Geigle and Lenzing). Using a theorem of Huebner and Lenzing we show, under a mild hypothesis, that if one considers coherent sheaves…

A relative Picard theory in the context of graded manifolds is introduced. A Berezinian calculus and a theory of connections over SUSY-curves are systematically developed, and used to prove a Gauss-Bonnet theorem for line bundles in that…

A correlational dialect is introduced within the quantum theory language to give a unified treatment of finite-dimensional informational/operational quantum theories, infinite-dimensional relativistic quantum theories, and quantum gravity.…

Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this…

The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well known result. A remarkable generalisation of this equivalence, due to Mackenzie, is the equivalence of principal bundle extensions with those…