Related papers: Cargese Lectures on Extra Dimensions
This is a set of four lectures presented at the Theoretical Advanced Study Institute (TASI-09) in June 2009. The goal of the lectures is to introduce students to some of the basic ideas and tools required for theoretical analysis of…
These are lecture notes based on the first part of a course on 'Mathematical Data Science', which I taught to final year BSc students in the UK in 2019-2020. Topics include: concentration of measure in high dimensions; Gaussian random…
This work is originally a Cambridge Part III essay. Throughout the paper, some aspects of General Relativity in higher dimensions are reviewed. The work presented draws a path within the wide landscape of higher dimensional black holes…
These lectures give a pedagogical review of dilaton gravity, Hawking radiation, the black hole information problem, and black hole pair creation. (Lectures presented at the 1994 Trieste Summer School in High Energy Physics and Cosmology)
Physical quantities and physical dimensions are among the first concepts encountered by students in their undergraduate career. In this pedagogical review, I will start from these concepts and, using the powerful tool of dimensional…
In this paper, we explicitly calculate the aether-like corrections for the electromagnetic field in the case when the space-time involves an extra compact spatial dimension besides of usual four dimensions. Our methodology is based on an…
A broader perspective is suggested for the study of higher dimensional cosmological models. [1986: Considerations involving the Einstein constraints and the Ricci form of the evolution equations for spatially homogeneous spacetimes in 4 or…
The hierarchy between the electroweak and Planck scales can be reduced when the extra dimensions are compactified with large volume or with warped geometry, resulting in the fundamental scale of the order of TeV. In such a scenario, one can…
Models for extra dimensions and some of the most promising ensuing signals for experimental discovery at the LHC are briefly reviewed. The emphasis will be put on the production of Kaluza Klein states from both flat and warped…
The standard model of particle physics represents the cornerstone of our understanding of the microscopic world. In these lectures we review its contents and structure, with a particular emphasis on the central role played by symmetries and…
These lectures cover aspects of primordial cosmology with a focus on observational tests of physics beyond the Standard Model. The presentation is divided into two parts: In Part I, we study the production of new light particles in the hot…
This presentation includes an introductory discussion of the unification of fundamental forces, properties of the elementary particles, Quantum Electrodynamics, the transition from Quantum Electrodynamics and Weak Interactions to…
We review results on several interesting phenomena in warped compactifications of M theory, as presented at Strings 2000. The behavior of gauge fields in dimensional reduction from $d+1$ to $d$ dimensions in various backgrounds is explained…
These lecture notes provide a pedagogical introduction, with exercises, to the techniques used in attempts to construct vacua with stabilised moduli in string theory. The reader is only assumed to have a basic knowledge of general…
As we typically teach in an introductory mechanics course, choosing a "good" reference frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely…
In these lectures we briefly cover some of the main lines of research in particle physics beyond the Standard Model.
We consider six dimensional brane world models with a compact and a warped extra dimension with five dimensional branes. We find that such scenarios have many interesting features arising from both ADD and Randall-Sundrum -models. In…
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
Methods of high-dimensional probability play a central role in applications for statistics, signal processing theoretical computer science and related fields. These lectures present a sample of particularly useful tools of high-dimensional…
The mechanism of continuous set of different universes formation is elaborated. It provides tool to solve the problem of observed smallness of physical parameters. Solution of two puzzles - the hierarchy and the cosmological constant…