Related papers: Quantum Spaces: Notes and Comments on a Lecture by…
The author has proposed five rules that permit conscious observers to be included in quantum mechanics. In the present paper, these rules are applied to the observation of a non-local pair of correlated particles. Rule (4) again prevents an…
These lectures present a brief introduction to measurement theory for QFT in possibly curved spacetimes introduced by the author and R. Verch [Comm. Math. Phys. 378 (2020) 851-889]. Topics include: a brief introduction to algebraic QFT,…
We show some basic results on the characterization of quasi-Polish spaces in terms of spaces of ideals, with an emphasis on the connections with computable topology.
These are the lecture notes for a short course on geometric quantization given by the author at the XVIII Modave Summer School on Mathematical Physics, Sep 5 - Sep 9.
Attention is focused on quantum spaces of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. Each of these quantum spaces can be…
These are extended lecture notes of the quantum mechanics course which I am teaching in the Weizmann Institute of Science graduate physics program. They cover the topics listed below. The first four chapter are posted here. Their content is…
Based on past contributions by Robert Schrader and Michael Karowski I review the problem of existence of interacting quantum field theory and present recent ideas and results on rigorous constructions.
This entry reviews Rudolf Carnap's philosophical views on the quantum mechanics of his time. It also offers some thoughts on how Carnap might have reacted to some recent developments in the foundations of quantum mechanics.
The notes contain a streamlined account on stability of univariate polynomials and related problems
Two lectures given at the UK-Japan Winter School on 'Geometry and Analysis Towards Quantum Theory', Durham, January 2004.
Lecture notes from the mini-course "Topics in Lorentz Geometry" taught at the University of S\~{a}o Paulo, in March/2019. The text has three parts: (i) an overall view of linear algebra in the pseudo-Euclidean space $\mathbb{R}^n_\nu$, with…
We use countable metric spaces to code Polish metric spaces and evaluate the complexity of some statements about these codes and of some relations that can be determined by the codes. Also, we propose a coding for continuous functions…
This is a position paper written as an introduction to the special volume on quantum algorithms I edited for the journal Mathematical Structures in Computer Science (Volume 20 - Special Issue 06 (Quantum Algorithms), 2010).
This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The…
In this article we present explicit formulae for q-differentiation on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. The…
This is an essay review of the book by D. Home: "Conceptual Foundations of Quantum Physics: An Overview from Modern Perspectives" (New York: Plenum Press, 1997), xvii+386 pp., ISBN 0-306-45660-5.
An extended text of the talk given at the conference ``2001: A Spacetime Odyssey'', to be published in the Proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, 21-25 May…
In this short note we provide a review of some developments in the area of homotopy quantum field theories, loosely based on a talk given by the second author at the Xth Oporto Meeting on Geometry, Topology and Physics.
These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…
The present work is a brief review of the recent development in the relativistic quantum mechanics in the $(1/2)\oplus (0,1/2)$ representation space. It can be useful for graduate students in particle physics and quantum field theory.