相关论文: Diagrammatics of Braided Group Gauge Theory

We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzezinski and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. We…

We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…

We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…

A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing…

It is shown that every quantum principal bundle is braided, in the sense that there exists an intrinsic braid operator twisting the functions on the bundle. A detailed algebraic analysis of this operator is performed. In particular, it…

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…

An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.

In this work we explore the geometrical interpretation of gauge theories through the formalism of fiber bundles. Moreover, we conduct an investigation in the topology of fiber bundles, providing a proof of the Classification Theorem. In the…

The underlying mathematical structures of gauge theories are known to be geometrical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles. It is now…

We recall the emergence of a generalized gauge theory from a noncommutative Riemannian spin manifold, viz. a real spectral triple $(A,H,D;J)$. This includes a gauge group determined by the unitaries in the $*$-algebra $A$ and gauge fields…

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent…

We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such…

We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories, and non-invariant theories satisfying two…

We investigate an interplay between some ideas in traditional gauge theory and certain concepts in fibered categories. We accomplish this by introducing a notion of a principal Lie 2-group bundle over a Lie groupoid and studying its…

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…

A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is…

We propose a conceptually economical and computationally tractable completion of the foundations of gauge theory on quantum principal bundles \`{a} la Brzezi\'{n}ski--Majid to the case of general differential calculi and strong bimodule…

The geometry of graded principal bundles is discussed in the framework of graded manifold theory of Kostant-Berezin-Leites. In particular, we prove that a graded principal bundle is globally trivial if and only if it admits a global graded…

Generalized geometry finds many applications in the mathematical description of some aspects of string theory. In a nutshell, it explores various structures on a generalized tangent bundle associated to a given manifold. In particular,…

Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…