相关论文: Cargese Lectures on Extra Dimensions
Much recent attention has focused on theories with large extra compactified dimensions. However, while the phenomenological implications of the volume moduli associated with such compactifications are well understood, relatively little…
These lectures on the combinatorics and geometry of 0/1-polytopes are meant as an \emph{introduction} and \emph{invitation}. Rather than heading for an extensive survey on 0/1-polytopes I present some interesting aspects of these objects;…
The aim of these notes (which were partially covered in lectures given at the Peyresq Summer School on 17--22 June, 2002) is to give an introduction to some mathematical aspects of supersymmetry. Some (hopefully) original point of view are…
Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think…
This set of lecture notes constitutes the free textbook project I initiated towards the end of Summer 2015, while preparing for the Fall 2015 Analytical Methods in Physics course I taught to upper level undergraduates at the University of…
We study a $(4+D)$-dimensional Kaluza-Klein cosmology with a Robertson-Walker type metric having two scale factors $a$ and $R$, corresponding to $D$-dimensional internal space and 4-dimensional universe, respectively. By introducing an…
This is a preliminary version, comments and inputs are welcome. Contents: 1. Introduction. 2. Fuzzy Spaces. 3. Star Products. 4. Scalar Fields on the Fuzzy Sphere. 5. Instantons, Monopoles and Projective Modules. 6. Fuzzy Nonlinear Sigma…
Students, after they leave our care, are called to solve the diverse problems of the world, so we should teach to increase transfer: the ability to apply fundamental principles to new problems and contexts. This ability is rare. The…
These notes are based on lectures given at the Erwin-Schrodinger Insitut in Vienna in 2006/07 and at the 2007 School on Attractor Mechanism in Frascati. Lecture I: special geometry from the superconformal point of view. Lecture II: black…
These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as…
Physics has a reputation among majority of life sciences students for being very complicated and tough. If we leave students with this impression, it is likely that students see physics class as useless and irrelevant to life sciences.…
Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that…
A central aim of theoretical physics is to account for the structure of matter at the most elementary level as underlying the Standard Model of particle physics, and ideally also as a basis for a substantial dark sector, as distributed in…
Planck scale physics represents a future challenge, located between particle physics and general relativity. The Planck scale marks a threshold beyond which the old description of spacetime breaks down and conceptually new phenomena must…
This set of five lectures provides an introduction to regularity structures and their use for the study of singular stochastic partial differential equations. Two appendices provide some additional informations that enter in the main text…
In the present work we intend to introduce a system based on VR (Virtual Reality) for examining analytical-geometric structures that occur in the study of mathematics and physics concepts in the last high school classes. In our opinion, an…
This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
This is a pedagogical exposition of holonomy groups intended for physicists. After some pertinent definitions, we focus on special holonomy manifolds, two per division algebras, and comment upon several cases of interest in physics,…
We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of…