Related papers: The $k\cdot p$ model: a short overview for beginne…
We describe a simple experimental apparatus which allows one to observe the wave properties of light in a new way. This apparatus also makes possible to introduce and illustrate, in a very suggestive way, some fundamental principles of…
The basic concepts of neutrino physics are presented at a level appropriate for integration into elementary courses on quantum mechanics and/or modern physics.
This textbook is an introduction to economic networks, intended for students and researchers in the fields of economics and applied mathematics. The textbook emphasizes quantitative modeling, with the main underlying tools being graph…
This series of introductory lectures consists of two parts. In the first part, I rapidly review the basic notions of quantum physics and many primitives of quantum information (i.e. notions that one must be somehow familiar with in the…
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.
The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.
A method is presented which makes considerably more transparent possible patterns behind low-energy scattering data. In particular, structures associated with resonances, such as locations, widths and heights, become visible with a naked…
This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…
Lectures notes in universal algebraic geometry for beginners
The history is described of how one of the most commonly used electric circuit components, an ordinary electric contact, has become a powerful tool for the physicists to study various mechanisms of electron scattering in metals. The…
This is a write-up of lectures intended for (under)graduate students. Contents: Scalar Ansatz (KP hierarchy). Fermionic Fock space. Fermi-Bose correspondence. KP hierarchy via free fermions. Formal distributions and locality. Operator…
This set of lecture notes first gives an introduction to the geometry of principal bundles. Next, it demonstrates how they can be used to formalize the concept of gauge theories arising in physics. A basic familiarity with the differential…
These lectures introduce the basic ideas and practices of statistical analysis for particle physicists, using a real-world example to illustrate how the abstractions on which statistics is based are translated into practical application.
We generalize the notion of linear chord diagrams to the case of matched sets of size $k$, which we call $k$-chord diagrams. We provide formal generating functions and recurrence relations enumerating these $k$-chord diagrams by the number…
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…
In the one-dimensional periodic potential case, we formulate the condition of Bloch periodicity for the reduced action by using the relation between the wave function and the reduced action established in the context of the equivalence…
The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.
A brief presentation of basic definitions and notation used in permutation patterns research.
This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…