Topic
Connection (vector bundle)
About: Connection (vector bundle) is a research topic. Over the lifetime, 917 publications have been published within this topic receiving 12846 citations. The topic is also known as: Koszul connection.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this article, it was shown that the geometrical phase factor found by Berry in his study of the quantum adiabatic theorem is precisely the holonomy in a Hermitian line bundle.
Abstract: It is shown that the "geometrical phase factor" recently found by Berry in his study of the quantum adiabatic theorem is precisely the holonomy in a Hermitian line bundle since the adiabatic theorem naturally defines a connection in such a bundle. This not only takes the mystery out of Berry's phase factor and provides calculational simple formulas, but makes a connection between Berry's work and that of Thouless et al. This connection allows the author to use Berry's ideas to interpret the integers of Thouless et al. in terms of eigenvalue degeneracies.
1,964 citations
1,241 citations
TL;DR: In this paper, an equivalent linearization technique to obtain the response of non-linear multi-degree-of-freedom dynamic systems to stationary gaussian excitations is developed, where the nonlinearities are assumed to be single-valued functions of accelerations, velocities and displacements.
Abstract: An equivalent linearization technique to obtain the response of non-linear multi-degree-of-freedom dynamic systems to stationary gaussian excitations is developed. The non-linearities are assumed to be single-valued functions of accelerations, velocities and displacements. Using a property of gaussian vector processes, the closed forms of the coefficients of the equivalent linear system are obtained by the direct application of partial differentiation and expectation operators to the non-linear terms. It is shown that when the non-linearities possess potentials, the linear system has symmetric coefficient matrices. A geometrical interpretation of the linear coefficients, in connection with the original non-linearities, is presented. The accuracy is investigated by means of examples.
365 citations
TL;DR: In this article, a method for analysing the behavior of flexibly-connected plane steel frames is presented, where two types of elements are used in the analysis procedure: the beamcolumn (frame) element and the connection element.
194 citations
TL;DR: In this article, the Yang-Mills action on a trivial quantum principal bundle is investigated and the moduli space of critical points of this action functional is independent of the q-dependent hermitian metric.
Abstract: A gauge invariant notion of a strong connection is presented and characterized. It is then used to justify the way in which a global curvature form is defined. Strong connections are interpreted as those that are induced from the base space of a quantum bundle. Examples of both strong and non-strong connections are provided. In particular, such connections are constructed on a quantum deformation of the two-sphere fibrationS
2→RP
2. A certain class of strongU
q
(2)-connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with theq-dependent hermitian metric. A particular form of the Yang-Mills action on a trivialU
q
(2)-bundle is investigated. It is proved to coincide with the Yang-Mills action constructed by A. Connes and M. Rieffel. Furthermore, it is shown that the moduli space of critical points of this action functional is independent ofq.
186 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 43 |
| 2020 | 32 |
| 2019 | 23 |
| 2018 | 32 |
| 2017 | 25 |