These notes are an expanded version of a short course of lectures given for graduate students in particle physics at Oxford. The level was intended to be appropriate for students in both experimental and theoretical particle physics.
These are lecture notes for a master-level course given at KTH, Stockholm, in the spring of 2017, with the primary aim of proving the stability of matter from first principles using modern mathematical methods in many-body quantum mechanics. General quantitative formulations of the uncertainty and the exclusion principles of quantum mechanics are introduced...
This book is an attempt to help students transform all of the concepts of quantum mechanics into concrete computer representations, which can be constructed, evaluated, analyzed, and hopefully understood at a deeper level than what is possible with more abstract representations.
Notes from the lectures by the author at the 7th Jerusalem Winter School 1990 on Quantum Cosmology and Baby Universes. The lectures covered quantum mechanics for closed systems like the universe, generalized quantum mechanics, time in quantum mechanics, the quantum mechanics spacetime, and practical quantum cosmology.
The book is based largely on the author's researches presented at conferences in the period 1992 onwards. It is a historically based exposition and an extension of the hyperbolic version of special relativity first proposed by Varicak (1910 etc) and others not long after the appearance of the early papers of Einstein and Minkowski.
We consider 42 fundamental questions which must be answered on the road to full enlightenment, and we attempt a first draft (or personal selection) of these ultimate questions, on topics ranging from the cosmological constant and origin of the universe to the origin of life and consciousness.
This contribution introduces the reader to the reformulation of Einstein's field equations of General Relativity as a constrained evolutionary system of Hamiltonian type and discusses some of its uses, together with some technical and conceptual aspects. Attempts were made to keep the presentation self contained and accessible to first-year graduate students.
This document gathers the notes of a 30-hour review course on gravitation. Its main goal is to propose a big picture of gravitation, where Einstein's relativity arises as a natural increment to Newton's theory. It is designed for bachelor/master students who do not necessarily have prior knowledge about relativity.
In recent years considerable advances have been made in quantitative homogenization of partial differential equations in the periodic and non-periodic settings. This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients...
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online.
Stylolites are ubiquitous geo-patterns observed in rocks in the upper crust, from geological reservoirs in sedimentary rocks to deformation zones, in folds, faults, and shear zones. These rough surfaces play a major role in the dissolution of rocks around stressed contacts, the transport of dissolved material and the precipitation in surrounding pores.
My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. My focus is to help modify your thinking of how math is used, rather than just pummel you with algorithms for you to memorize without giving you the proper context for such algorithms.
Cosmology and particle physics are deeply interrelated. Among the common problems are dark energy, dark matter and baryon asymmetry of the Universe. We discuss these problems in general terms, and concentrate on several particular hypotheses.
This is an introductory course about random matrices. These notes will give the reader a smell of that fascinating tool for physicists and mathematicians that are Random Matrices, and they can give the envy to learn and search more.
As shape analysis of the form presented in Srivastava and Klassen's textbook 'Functional and Shape Data Analysis' is intricately related to Lebesgue integration and absolute continuity, it is advantageous to have a good grasp of the latter two notions. Accordingly, in these notes we review basic concepts and results about Lebesgue integration and absolute continuity.
This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the Internet. There is considerable discussion of TeX and other modern writing environments. We also consider electronic journals, print-on-demand books, Open Access Journals, preprint servers, and many other aspects of modern publishing life.
An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 135 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide without leading to panic.
Probably the target audience is theoretical physicists, especially young ones, who may enjoy comparing my struggles with their own. It will probably have too much physics for a nontechnical reader, and too little for a physicist, but perhaps there will be different things for each.
This paper is an introduction to work motivated by the question 'can multipartite entanglement be detected by homological algebra?' We introduce cochain complexes associated to multipartite density states whose cohomology detects factorizability.
We give a pedagogical introduction to algebraic quantum field theory (AQFT), with the aim of explaining its key structures and features. Topics covered include: algebraic formulations of quantum theory and the GNS representation theorem, the appearance of unitarily inequivalent representations in QFT (exemplified by the van Hove model), the main assumptions of AQFT and simple models thereof, the spectrum condition, etc.
The main goal of these lectures is introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary orbits, wave-particle duality and probabilistic interpretation.
These notes describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the main focus lies in Euclidean field theory. The notion of Gaussian measure and the construction of the Wiener measure are covered.
We review the theory of hadronic atoms in QCD + QED, based on a non-relativistic effective Lagrangian framework. We first provide an introduction to the theory, and then describe several applications: meson-meson, meson-nucleon atoms and meson-deuteron compounds. Finally, we compare the quantum field theory framework used here with the traditional approach, which is based on quantum-mechanical potential scattering.
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this representation as a reference-and-imbedding-structure, the foundations of an intelligible reconstruction of the Hilbert-Dirac formulation of Quantum Mechanics is developed.
The aim of this review is to provide quantum engineers with an introductory guide to the central concepts and challenges in the rapidly accelerating field of superconducting quantum circuits. Over the past twenty years, the field has matured from a predominantly basic research endeavor to one that increasingly explores the engineering of larger-scale superconducting quantum systems.
I aim to make accessible the rules of the calculus of probability to those, unacquainted with the higher chapters of mathematics. The reading of my book will not require any other knowledge except elementary algebra, or even, strictly speaking, algebraic notation.
These lectures aim to provide a pedagogical introduction to the philosophical underpinnings and technical features of Effective Field Theory (EFT). Improving control of S-matrix elements in the presence of a large hierarchy of physical scales m<
In this review we explain the main methods and techniques of lattice perturbation theory, focusing on the cases of Wilson and Ginsparg-Wilson fermions. We will illustrate, among other topics, the peculiarities of perturbative techniques on the lattice, the use of computer codes for the analytic calculations and the computation of lattice integrals. Discussed are also methods for the computation of 1-loop integrals with very high precision.