Related papers: The Eightfold Way
A non-formal simply connected compact symplectic manifold of dimension 8 is constructed.
This book provides an introduction to path integral methods and their application to modeling atomistic processes. The book covers both the foundational theory and recently developed simulation techniques. The text provides a self-contained…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
We give six arguments that the Planck scale should be viewed as a fundamental minimum or boundary for the classical concept of spacetime, beyond which quantum effects cannot be neglected and the basic nature of spacetime must be…
This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics
An alternative elementary argument for the magnetic field outside a solenoid is described.
This is part one of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and…
Short survey to be published at the Encyclopedia of Mathematical Physics.
This is a short expository article on alternating knots and is to appear in the Concise Encyclopedia of Knot Theory.
A brief exposition of the point of higher topos theory in (mathematical) physics, commissioned for the Encyclopedia of Mathematical Physics 2nd ed.
The following notes are intended to provide a brief primer in plasma physics, introducing common definitions, basic properties and processes typically found in plasmas. These concepts are inherent in contemporary plasma-based accelerator…
The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential…
We give a quick tour through many of the classical results in the field of minimal submanifolds, starting at the definition. The field of minimal submanifolds remains extremely active and has very recently seen major developments that have…
These notes are an outgrowth of an advanced undergraduate course taught at the University of Maryland, College Park. They are intended as an introduction to various aspects of particle and nuclear physics with an emphasis on the role of…
A pedagological introduction to effective field theory is presented.
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
Short introduction to exotic differential structures on manifolds is given. The possible physical context of this mathematical curiosity is discussed. The topic is very interesting although speculative.
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
This is an expository article for the Encyclopedia of Mathematical Physics on the subject in the title.
A neutron optical experiment is presented to investigate the paths taken by neutrons in a three-beam interferometer. In various beam-paths of the interferometer, the energy of the neutrons is partially shifted so that the faint traces are…