started an entry *Bohmian mechanics* (prompted by discussion in another thread)

I have started something at Bohr-Sommerfeld leaf, but need to continue later when I have more time and energy

]]>started some minimum at *Bost-Connes system*.

Hm, it seems that the statement is that that partition function of the BC-system

$\beta \mapsto Tr(\exp(- \beta H_{BostConnes}))$is the Riemann zeta function. But by the pertinent analogies the zeta functions are not supposed to *equal* partition functions, but to be related to them by the transformation

Hm.

]]>created a currently fairly empty entry *quantum measurement*, just so as to have a place where to give a commented pointer to the article

- Klaas Landsman, Robin Reuvers,
*A Flea on Schrödinger’s Cat*, Found. Phys. 43, 373-407 (2013) (arXiv:1210.2353)

expanded the section *Idea – In brief* at *Bohr topos* just a little bit, in order to amplify the relation to Jordan algebras better (which previously was a bit hidden in entry).

I have been touching and editing a bit more the circle of entries on the foundations of quantum mechanics which all revolve around the phenomenon that the space of states in quantum mechanics is all determined (just) by the Jordan algebra structure on the algebra of observables, and notably by the poset of commutative subalgebras of the algebra of observables:

The last of these entries is new, but essentially just split-off from “poset of commutative subalgebras” for the moment. The other entries in the list I have mildly edited, mainly cross-linking them with each other. At *Kochen-Specker theorem* I did a bit more editing, but mainly just trying to prettify the formatting and the layout of the paragraphs and cross-links..

I wanted to do more, but I am running of out time now.

Anyway, I think together these theorems paint a picture that is noteworthy and hasn’t been highlighted much. The proponents of looking at QM through the ringed topos over os poset of commutative subalgebras highlight Kochen-Specker, but I find Gleason’s theorem is actually a *stronger* argument for this approach, while Kochen-Specker is then more of a nice spin-off. Also Alfsen-Shultz combined with Harding-Döring-Hamhalter is essentially a re-formulation of Gleason that amplifies more the poset structure on the poset of commutative subalgebras.

Here Gleason and, via Jordan, Alfsen-Shultz of course go back to the very roots of QM in the 1950s, whereas Döring et al is recent. This is maybe noteworthy.

More later. Have to run now.

]]>started *Guillemin-Sternberg geometric quantization conjecture*

So far just the brief Idea and a few commented references.

]]>Stub for Morse potential.

]]>I have given *interaction picture* genuine content (the entry used to be effectively empty):

gave it one section “In quantum mechanics” with the standard kind of material going from interacting Hamiltonians to the definition of the S-matrix, and then a section “In quantum field theory” with an outline of which steps in the previous discussion require special technical care and how.

In the process I expanded the entry *Dyson formula*. (In the end I effectively rewrote it, but now with a little broader perspective and more pointers).

I gave *Fedosov deformation quantization* its own entry, so far with an Idea-section putting the construction in perspective, an informal outline of how the method proceeds, and some references.

Circumstances prompted me to write a kind of pamphlete pointing out some aspects that seem worth taking notice of have not found much appreciation yet:

This surveys how basic theorems about the standard foundation of quantum mechanics imply an accurate geometric incarnation of the “phase space in quantum mechanics” by an order-theoretic structure that combines with an algebraic structure to a ringed topos, the “Bohr topos”. While the notion of Bohr topos has been *motivated* by the Kochen-Specker theorem, the point here is to highlight that taking into account further theorems about the standard foundations of quantum mechanics, the notion effectively follows automatically and provides an accurate and useful description of the geometry of “quantum phase space” also in quantum field theory.