相关论文: Living with Infinities

Current thinking on the interpretation of quantum physics is reviewed, with special detail given to the Copenhagen and Everett many-worlds interpretations.

Talk presented at the conference ``Historical and Philosophical Reflections on the Foundations of Quantum Field Theory,'' at Boston University, March 1996. It will be published in the proceedings of this conference.

In this essay I discuss certain analogies between quantum incompatibility and entanglement. It is an expanded version of my talk presented at Mathematical Foundations of Quantum Mechanics in memoriam Paul Busch, held in York in June 2019.

This paper records my opening remarks at Nobel Symposium 148, on Graphene and Quantum Matter, at Saltsj\"obaden, Sweden, in June 2010. After some broad comments on the quantum theory of matter as a frontier of physics, and some slightly…

These notes grew from a series of lectures given by the authors during the last decade. They will be published in the proceedings of TASI 2021. After a brief introduction to quantum information theory tools, they are organized in four…

These notes are based on a talk given at the Summer School "Infinite-dimensional representations of finite-dimensional algebras" held at the University of Manchester in September 2015. They intend to provide a brief introduction to the…

This is an extended abstract of my talk at the Oberwolfach-Workshop "Representation Theory of Finite-Dimensional Algebras" (February 6 - 12, 2005). It gives self-contained and simplified definitions of quantum cluster algebras introduced…

The mathematical study of infinity seems to have the ability to transport the mind to lofty and unusual realms. Decades ago, I was transported in this way by Rudy Rucker's book Infinity and the Mind. Despite much subsequent learning and…

This is the written version of the opening talk at the symposium "Expectations of a Final Theory," at Trinity College, Cambridge, on September 2, 2005. It is to be published in Universe or Multiverse?, ed. B. Carr (Cambridge University…

The quantization of gravity offers a solution to the presence of singularities in cosmology. Infinities are removed because of the existence of finite quanta of spacetime. This is one of the most important prediction of Loop Quantum…

An assessment of the anthology, 'Many Worlds? Everett, Quantum Theory and Reality', edited by Simon Saunders, Jonathan Barrett, Adrian Kent and David Wallace.

I sketch what it is supposed to mean to quantize gauge theory, and how this can be made more concrete in perturbation theory and also by starting with a finite-dimensional lattice approximation. Based on real experiments and computer…

We describe the modern approach to quantum cosmology, as initiated by Hartle and Hawking, Linde, Vilenkin and others. The primary aim is to explain how one determines the consequences for the late universe of a given quantum theory of…

We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum…

I review the tunneling, Hartle-Hawking and Linde proposals for the wave function of the universe and comment on the recent work on quantum creation of open universes.

I present my encounter with John Bell at CERN, our collaboration and joint work in particle physics. I also will recall our quantum debates and give my personal view on Bell's fundamental work on quantum theory, in particular, on…

In this article we will review some notions of infiniteness that appear in Hilbert space operators and operator algebras. These include proper infiniteness, Murray von Neumann's classification into type I and type III factors and the class…

In this talk, we give a glimpse of the problems with quantum gravity and some possible solutions.

This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…

We analyze on the formalism of probability measures -functional integrals on function spaces , the problem of infinities on Euclidean field theories