Related papers: Quantum Spaces: Notes and Comments on a Lecture by…
These lecture notes were prepared for a mixed audience of students, postdocs and faculty from the Indian Institute of Technology Madras, India and neighboring institutions, particularly the Institute of Mathematical Sciences. I am not an…
This set of lecture notes gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations. Later sections describe more advanced…
We describe postulates for a novel realist version of relativistic quantum theory or quantum field theory in Minkowski space or other background spacetimes with suitable asymptotic properties. We illustrate their application in toy models.
The talks given in parallel session D4 at the 20th International Conference on General Relativity and Gravitation (Warsaw 2013) are summarized.
This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied…
A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.
I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and…
The notes provide a short introduction to de Branges--Rovnyak spaces. They cover some basic facts and are intended to give the reader a taste of the theory, providing sufficient motivation to make it interesting.
These lecture notes are intended to give a modest impulse to anyone willing to start or pursue a journey into the theory of Vertex Algebras by reading one of Kac's or Lepowsky-Li's books. Therefore, the primary goal is to provide required…
The main goal of these lectures -- 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…
These are notes from a jointly taught class at the University of Chicago and lectures by the first author in Santa Cruz. Topics covered include: construction of moduli spaces of stable maps, Gromov-Witten invariants, quantum cohomology, and…
These are lecture notes from author's mini-course during Session 1: "Vertex algebras, W-algebras, and application" of INdAM Intensive research period "Perspectives in Lie Theory", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa,…
We present some informal remarks on aspects of relativistic quantum computing.
The first version of these lecture notes is based on the hand-written notes I prepared for the cosmology course taught to graduate students of PPGFis and PPGCosmo at the Federal University of Esp\'irito Santo (UFES), starting in 2014. The…
Comment on the Letter ``Polynomial-Time Simulation of Pairing Models on a Quantum Computer'', L. A. Wu, M. S. Byrd and D. A. Lidar, Phys. Rev. Lett. 89, 057904 (2002).
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
This article gives an elementary introduction to quantum computing. It is a draft for a book chapter of the "Handbook of Nature-Inspired and Innovative Computing", Eds. A. Zomaya, G.J. Milburn, J. Dongarra, D. Bader, R. Brent, M.…
For differential calculi over certain right coideal subalgebras of quantum groups the notion of quantum tangent space is introduced. In generalization of a result by Woronowicz a one to one correspondence between quantum tangent spaces and…
These are notes from introductory lectures at the graduate school "Topological Quantum Groups" in B\k{e}dlewo (June 28--July 11, 2015). The notes present the passage from Hopf algebras to compact quantum groups and sketch the notion of…
This is a written version of a series of lectures aimed at undergraduate students in astrophysics/particle theory/particle experiment. We summarize the important progress made in recent years towards understanding high energy astrophysical…