Magnetic monopoles and vortices in the standard model of electroweak interactions

These lectures start with an elementary introduction to the subject of magnetic monopoles which should be accesible from any physics background. In the Weinberg-Salam model of electroweak interactions, magnetic monopoles appear at the ends of a type of non-topological vortices called electroweak strings. These will also be discussed, as well as recent simulations of their formation during a phase transition which indicate that, in the (unphysical) range of parameters in which the strings are classically stable, they can form with a density comparable to topological vortices.Comment: 19 pages, Les Houches lectures, NATO-ASI on Topological defects and the non-equilibrium dynamics of symmetry breaking phase transitions, Feb. 9

Solitons as Key Parts to Produce a Universe in the Laboratory

Cosmology is usually understood as an observational science, where experimentation plays no role. It is interesting, nevertheless, to change this perspective addressing the following question: what should we do to create a universe, in a laboratory? It appears, in fact, that this is, in principle, possible according to at least two different paradigms; both allow to circumvent singularity theorems, i.e. the necessity of singularities in the past of inflating domains which have the required properties to generate a universe similar to ours. The first of them is substantially classical, and is built up considering solitons which collide with surrounding topological defects, generating an inflationary domain of space-time. The second is, instead, partly quantum and considers the possibility of tunnelling of past-non-singular regions of spacetime into an inflating universe, following a well-known instanton proposal. We are, here, going to review some of these models, as well as highlight possible extensions, generalizations and the open issues (as for instance the detectability of child universes and the properties of quantum tunnelling processes) that still affect the description of their dynamics. In doing so we will remark how the works on this subject can represent virtual laboratories to test the role that fundamental principles of physics (particularly, the interplay of quantum and general relativistic realms) played in the formation of our universe.Comment: Based on a talk given at the 2006 Biennial Meeting of the International Association for Relativistic Dynamics (IARD06). 11 pages, LaTe

Causal Fermion Systems as a Candidate for a Unified Physical Theory

The theory of causal fermion systems is an approach to describe fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. We here give a non-technical introduction.Comment: 19 pages, LaTeX, minor improvements (published version

Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints

This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns from non-locality and anisotropy of the interactions among individuals. A mathematical technique by time-evolving measures is introduced to deal with both macroscopic and microscopic scales within a unified modeling framework. Then self-organization issues are investigated and numerically reproduced at the proper scale, according to the kind of agents under consideration.Comment: 24 pages, 13 figure

Jet Methods in Time-Dependent Lagrangian Biomechanics

In this paper we propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds associated to the extended musculo-skeletal configuration manifold, called the configuration bundle. We start with an ordinary configuration manifold of human body motion, given as a set of its all active degrees of freedom (DOF) for a particular movement. This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. By this extension, using techniques from fibre bundles, we defined the biomechanical configuration bundle. On the biomechanical bundle we define vector-fields, differential forms and affine connections, as well as the associated jet manifolds. Using the formalism of jet manifolds of velocities and accelerations, we develop the time-dependent Lagrangian biomechanics. Its underlying geometric evolution is given by the Ricci flow equation. Keywords: Human time-dependent biomechanics, configuration bundle, jet spaces, Ricci flowComment: 13 pages, 3 figure