Jonathan Gleason (1989-2018) received his Bachelor’s degree from the University of Chicago, his Master’s from Cambridge University in Cambridge, England, and at the time of his death was a fifth year Grad student at the University of California, Berkeley.
In two unpublished notes (see below), Gleason was concerned with the motivation of the mathematical foundations of algebraic quantum mechanics:
[Gleason (2011), p. 12]:
“In Mackey (1963), immediately after stating what he believes to be an unmotivated axiom that invokes in some way the usual Hilbert space formulation of quantum mechanics, the author states the following:
‘Ideally one would like to have a list of physically plausible assumptions from which one could deduce [this axiom]. […]’
The problem he is referring to is a problem that has bothered me ever since I first learned quantum mechanics, and while I do not think the argument we have just given is as strong an argument as Mackey is referring to, in my opinion, it is damn well close, and indeed, close enough that this author will finally be able to sleep at night.“
On the foundations of quantum mechanics/quantum probability theory conceptualized algebraically in close analogy to classical mechanics/probability theory (with algebras of quantum observables understood as star-algebras and quantum states understood as states on a star-algebra):
Jonathan Gleason, The $C^*$-algebraic formalism of quantum mechanics (2009) [pdf, pdf]
Jonathan Gleason, From Classical to Quantum: The $F^\ast$-Algebraic Approach, contribution to VIGRE REU 2011, Chicago (2011) [pdf, pdf]
Created on July 4, 2023 at 14:34:22. See the history of this page for a list of all contributions to it.