Related papers: Quantum Fibre Bundles. An Introduction
This is a short, self-contained expository survey, focused on algebraic and analytic aspects of quantum groups. Topics covered include the definition of ``quantum group,'' the Yang-Baxter equation, quantized universal enveloping algebras,…
We survey known results on the canonical bundle formula and its applications in algebraic geometry.
We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than via mere representations of the structure group. We devise a notion of connection generalising Ehresmann…
Endomorphisms algebras can replace the concept of principal fiber bundle. Gauge theories are reformulated within this algebraic framework and further generalized to unify ordinary connections and Higgs fields. A 'noncommutative Maxwell'…
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…
Motivated by gauge theory, we develop a general framework for chain complex valued algebraic quantum field theories. Building upon our recent operadic approach to this subject, we show that the category of such theories carries a canonical…
Using the notion of generalized weight we improve estimates on the parameters of quantum codes obtained by Steane's construction from binary codes. This yields several new families of quantum codes.
This talk introduces a Cartan-geometric framework for generalised geometries governed by a differential graded Lie algebra. In contrast to ordinary Cartan geometry, the tangent bundle is extended and qu both a global duality group and a…
The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…
In this Note, we propose a line bundle approach to odd-dimensional analogues of generalized complex structures. This new approach has three main advantages: (1) it encompasses all existing ones; (2) it elucidates the geometric meaning of…
A fibre product construction is used to give a description of quantum line bundles over the generic Podles spheres by gluing two quantum discs along their boundaries. Representatives of the corresponding $K_0$-classes are given in terms of…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
I briefly review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles.
A procedure is described to associate fibre bundles over the circle to two- dimensional theories with defects which have their field equations and defects described by a zero curvature condition.
We explore factorizations of noncommutative Riemannian spin geometries over commutative base manifolds in unbounded KK-theory. After setting up the general formalism of unbounded KK-theory and improving upon the construction of internal…
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…
We discuss the fibre bundle of co-adjoint orbits of compact Lie groups, and show how it admits a compatible K\"ahler structure. The case of the unitary group allows us to reformulate the geometric framework of quantum information theory. In…
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
Around 1920, Kaluza and Klein had the idea to add a fifth dimension to the classical 4-dimensional spacetime of general relativity to create a geometric theory of gravitation and electromagnetism. Today, theoretical evidences, like string…