Kadison-Singer from mathematical physics: An introduction

This is a contribution to the webpage for an AIM 2006 Workshop on the Kadison-Singer Problem. The posted text will become a permanent Introduction for the record. The current version is written by Palle Jorgensen, following lectures at the meeting by Dick Kadison. The Introduction stresses how the mathematical context and the problem itself grew out of conceptual issues in quantum mechanics.

Editorial comment by Palle Jorgensen:

This is a draft of the Intro to the Kadison-Singer IMA website. It grew out of a workshop at the AIM institute (with NSF support) in Palo Alto in September, 2006.

Part of the workshop program is the creation of a permanent AIM website for the Kadison-Singer Problem, and I was assigned to write the first draft of an Introduction.

Several things guided me:

1. Motivation and history. This means that I left out mention of current trends, and that I did not include an updated Bibliography. This is left to the other writers for the project.
2. The exposition is close to the lecture presentation Professor R. V. Kadison gave at the 2006 IMA workshop itself.
3. It is close to the original KS 1959 paper, and it stresses Dirac's influence.
4. Physics, Paul Dirac, Dirac's book, and Dirac's thinking was central to the motivations. (The write-up should be understandable to physicists, for example workers in Quantum computation. It is clear that Dirac's views and notation are popular in these circles!)
These concerns mean that the present KS-Introduction will not talk much about a lot of other more recent applications of the KS-ideas, for example to signal processing. Others will write about that.
5. I wanted to bridge separate communities, pure vs. applied, math vs. physics, etc. To do that, I say a few things in ways that have become popular with physicists, but perhaps aren't especially familiar to mathematicians.

This current draft is a "live" document and is likely to undergo a few more iterations.

Palle E. T. Jorgensen

This page was last modified on 20 November 2006 by Brian Treadway.

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