相关论文: Geometrical Methods in Gauge Theory

In this paper we study cobordism categories consisting of manifolds which are endowed with geometric structure. Examples of such geometric structures include symplectic structures, flat connections on principal bundles, and complex…

This is a review of exceptional field theory: a generalisation of Kaluza-Klein theory that unifies the metric and $p$-form gauge field degrees of freedom of supergravity into a generalised or extended geometry, whose additional coordinates…

The notion of a higher bundle gerbe is introduced to give a geometric realization of the higher degree integral cohomology of certain manifolds. We consider examples using the infinite dimensional spaces arising in gauge theories.

A new approach to the Kaluza theory and its relation to the gauge theory is presented. Two degenerate metrics on the $4+d$-dimensional total manifold are used, one corresponding to the spacetime metric and giving the fiber of the gauge…

This is the second in a series of papers intended to provide a basic overview of some of the major ideas in particle physics. Part I [arXiv:0810.3328] was primarily an algebraic exposition of gauge theories. We developed the group theoretic…

We define contact fiber bundles and investigate conditions for the existence of contact structures on the total space of such a bundle. The results are analogous to minimal coupling in symplectic geometry. The two applications are…

To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.

The fibre bundle formulation of gauge theory is generally accepted. The jet manifold machinery completes this formulation and provides the adequate mathematical description of dynamics of fields represented by sections of fibre bundles.…

We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.

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.

We develop a linearized five dimensional Kaluza-Klein theory as a gauge theory. By perturbing the metric around flat and the De Sitter backgrounds, we first discuss linearized gravity as a gauge theory in any dimension. In the particular…

We will show that gauge theory can be described by an almost product structure, which is a certain type of endomorphism of the tangent bundle. We will recover the gauge field strength as the Nijenhuis tensor of this endomorphism. We discuss…

We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.

This survey article is an invited contribution to the Encyclopedia of Mathematical Physics, 2nd edition. We provide an accessible overview on relevant applications of higher and derived geometry to theoretical physics, including higher…

I briefly review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles.

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 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 present a description of two dimensional Yang-Mills gauge theory on the plane and on compact surfaces, examining the topological, geometric and probabilistic aspects.

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…

Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular,…