Related papers: Geometrical Methods in Gauge Theory

We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…

We construct gauge theories in two extra dimensions compactified on the chiral square, which is a simple compactification that leads to chiral fermions in four dimensions. Stationarity of the action on the boundary specifies the boundary…

In this short paper, we will review the proposal of a correspondence between the doubled geometry of Double Field Theory and the higher geometry of bundle gerbes. Double Field Theory is T-duality covariant formulation of the supergravity…

It is well-known that principal bundles and associated bundles underlie the geometric structure of classical gauge field theories. In this paper, we explore the reformulation of gauge theories in terms of Lie algebroids and their associated…

This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…

Higher bundles are homotopy coherent generalisations of classical fibre bundles. They appear in numerous contexts in geometry, topology and physics. In particular, higher principal bundles provide the geometric framework for higher-group…

In this note, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk-Mrcun and establish its relation with the existing physics literature. In…

In Kaluza derived theories the electromagnetic potential is interpreted as a part of the metric in a higher dimensional theory of gravity. Here we present a more Yang-Mills like unification of classical electromagnetism and gravity within…

Recently, a new gauging procedure called Sculpting mechanism was proposed to obtain the M-theory origin of type II gauged Supergravity theories in 9D. We study this procedurein detail and give a better understanding of the different…

Topological principles constitute at present an integral component of condensed matter physics, permeating the modern characterization of electronic states while also guiding materials design. In this brief Perspective, I highlight three…

We first generalize the operation of formal exterior differential in the case of finite dimensional fibered manifolds and then we extend it to certain bundles of smooth maps. In order to characterize the operator order of some morphisms…

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…

Consider a fiber bundle in which the total space, the base space and the fiber are all symplectic manifolds. We study the relations between the quantization of these spaces. In particular, we discuss the geometric quantization of a vector…

In the present paper we study some homotopy invariants which can be defined by means of bundles with fiber a matrix algebra. We also introduce some generalization of the Brauer group in the topological context and show that any its element…

We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended…

This series of lectures is planned as a generalization of author's large (more than fifteen years) experience of work in the theoretical physics. The modern theoretical physics is based on the group-theoretical approach which generates the…

The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic…

We consider how gauge theories can be described by matrix models. Conventional matrix regularization is defined for scalar functions and is not applicable to gauge fields, which are connections of fiber bundles. We clarify how the degrees…

We study two-dimensional topological gauge theories with gauge group equal to the symmetric group $S_n$ and their string theory duals. The simplest such theory is the topological quantum field theory of principal $S_n$ fiber bundles. Its…

I describe the Kaluza-Klein approach to general relativity of 4-dimensional spacetimes. This approach is based on the (2,2)-fibration of a generic 4-dimensional spacetime, which is viewed as a local product of a (1+1)-dimensional base…