Related papers: Montreal Lecture Notes on Quadratic Fourier Analys…
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
These notes are based on a lecture course by L. Chekhov held at the University of Manchester in May 2006 and February-March 2007. They are divulgative in character, and instead of containing rigorous mathematical proofs, they illustrate…
These notes basically contain a material of two mini--courses which were read in G\"{o}teborg in April 2015 during the author visit of Chalmers & G\"{o}teborg universities and in Beijing in November 2015 during "Chinese--Russian Workshop on…
This article presents a convenient approach to Fourier analysis for the investigation of functions and distributions defined in $\mathbb{T}^m \times \mathbb{R}^n$. Our approach involves the utilization of a mixed Fourier transform,…
These notes reflect the contents of three lectures given at the workshop of the 14th International Conference on Representations of Algebras (ICRA XIV), held in August 2010 in Tokyo. We first provide an introduction to quantum loop algebras…
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
In these lectures I cover various aspects of Chiral Symmetry in the hadronic world from a pre-QCD perspective. I also discuss the absence of spontaneous symmetry breaking in d=4 large N O(N) models.
These are lecture notes presented at the 2017 CTEQ Summer School at the University of Pittsburgh and the 2018 CTEQ Summer School at the University of Puerto Rico, Mayaguez. The title is a reference to hep-th/0309149 and introduces…
The ongoing progress in quantum technologies has fueled a sustained exploration of their potential applications across various domains. One particularly promising field is quantitative finance, where a central challenge is the pricing of…
Now that lattice QCD simulations are able to include effects of light sea quarks, the prospects are good for constraining quark flavor phenomenology. This review talk for particle physics experimentalists begins with an introduction…
This report is a combined version of two talks presented by the authors at the Edinburgh $b$-physics Workshop, December 1991. It presents the ideas of heavy quark symmetry and gives an introduction to some applications. The references…
These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.
These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these…
This is a series of lectures on Monte Carlo results on the non-perturbative, lattice formulation approach to quantum field theory. Emphasis is put on 4D scalar quantum field theory. I discuss real space renormalization group, fixed point…
We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split…
These are the notes for a minicourse held in Odessa (2016) and Belo Horizonte (2017). My aim was to provide a short introduction to basic notions of category theory and representation theory of finite-dimensional algebras. We learnt the…
This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo…
These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.
Lectures at the CRM-CAP Summer School 'Particles and Fields 94' August 16-24 1994, Banff, Alberta, Canada.