Categories and the Foundations of Classical Field Theories

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills theories.Comment: 26 pages. Written for a volume entitled "Categories for the Working Philosopher", edited by Elaine Landr

Volume integral equations for electromagnetic scattering in two dimensions

We study the strongly singular volume integral equation that describes the scattering of time-harmonic electromagnetic waves by a penetrable obstacle. We consider the case of a cylindrical obstacle and fields invariant along the axis of the cylinder, which allows the reduction to two-dimensional problems. With this simplification, we can refine the analysis of the essential spectrum of the volume integral operator started in a previous paper (M. Costabel, E. Darrigrand, H. Sakly: The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body, Comptes Rendus Mathematique, 350 (2012), pp. 193-197) and obtain results for non-smooth domains that were previously available only for smooth domains. It turns out that in the TE case, the magnetic contrast has no influence on the Fredholm properties of the problem. As a byproduct of the choice that exists between a vectorial and a scalar volume integral equation, we discover new results about the symmetry of the spectrum of the double layer boundary integral operator on Lipschitz domains.Comment: 21 page

Fundamental Symmetries and Interactions - Some Aspects

In the framework of nuclear physics and at nuclear physics facilities a large number of different experiments can be performed which render the possibility to investigate fundamental symmetries and interactions in nature. In particular, the precise measurements of properties of fundamental fermions, searches for new interactions in $\beta$-decays, and violations of discrete symmetries have a robust discovery potential for physics beyond standard theory. Precise measurements of fundamental constants can be carried out as well. Low energy experiments allow probing of New Physics models at mass scales far beyond the reach of present accelerators or such planned for the future in the domain of high energy physics and at which predicted new particles could be produced directly.Comment: Review Talk ENAM'0

Global aspects of gravitomagnetism

We consider global properties of gravitomagnetism by investigating the gravitomagnetic field of a rotating cosmic string. We show that although the gravitomagnetic field produced by such a configuration of matter vanishes locally, it can be detected globally. In this context we discuss the gravitational analogue of the Aharonov-Bohm effect.Comment: 10 pages - Typeset using REVTE