Geometric magnetism in classical transport theory

Geometric Foundations of Classical Yang-mills Theory

We analyze the geometric foundations of classical YangMills theory by studying the relationships between internal relativity, locality, global/local invariance, and background independence. We argue that internal relativity and background independence are the two independent defining principles of Yang-Mills theory. We show that local gauge invariance – heuristically implemented by means of the...

A Geometric Approach to Classical Galois Theory

Geometric Control Theory and Classical Problems in Chemical Reactor Design

A classical problem in chemical reactor design can be stated roughly in the following way: Given a network of chemical reactions and a specified feed, how should one design a chemical reactor to enhance the production of certain desired species while suppressing the production of undesired ones? The purpose of this article is to describe recent work in which geometric control theory provides so...

Geometric magnetism in open quantum systems

An isolated classical chaotic system, when driven by the slow change in several parameters, responds with two reaction forces: geometric friction and geometric magnetism. By using the theory of quantum fluctuation relations, we show that this holds true also for open quantum systems and provide explicit expressions for those forces in this case. This extends the concept of Berry curvature to th...

A Geometric Hamilton-jacobi Theory for Classical Field Theories

In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for hamiltonian mechanics to the case of classical field theories in the framework of multisymplectic geometry and Ehresmann connections.