have expanded the Idea-section at *quantum logic* to now read as follows:

Broadly speaking, *quantum logic* is meant to be a kind of formal logic that is to traditional formal logic as quantum mechanics is to classical mechanics.

The first proposal for such a formalization was (Birkhoff-vonNeumann 1936), which suggested that given a quantum mechanical system with a Hilbert space of states, the logical propositions about the system are to correspond to (the projections to) closed subspaces, with implication given by inclusion of such subspaces, hence that quantum logic is given by the lattice of closed linear subspaces of Hilbert spaces.

This formalization is often understood as being the default meaning of “quantum logic”. But the proposal has later been much criticized, for its lack of key properties that one would demand of a formal logic. For instance in (Girard 11, page xii) it says:

Among the magisterial mistakes of logic, one will first mention quantum logic, whose ridiculousness can only be ascribed to a feeling of superiority of the language – and ideas, even bad, as soon as they take a written form – over the physical world. Quantum logic is indeed a sort of punishment inflicted on nature, guilty of not yielding to the prejudices of logicians… just like Xerxes had the Hellespont – which had destroyed a boat bridge – whipped.

and for more criticisms see (Girard 11, section 17).

Therefore later other proposals as to what quantum logic should be have been made, and possibly by “quantum logic” in the general sense one should understand any formal framework which is supposed to be able to *express* the statements whose semantics is the totality of all what is verifiable by measurement in a quantum system.

In particular it can be argued that flavors of *linear logic* and more generally *linear type theory* faithfully capture the essence of quantum mechanics (Abramsky-Duncan 05, Duncan 06, see (Baez-Stay 09) for an introductory exposition) due to its categorical semantics in symmetric monoidal categories such as those used in the desctiption of finite quantum mechanics in terms of dagger-compact categories. In particular the category of (finite dimensional) Hilbert spaces that essentially underlies the Birkhoff-vonNeumann quantum logic interprets linear logic.

Another candidate for quantum logic has been argued to be the internal logic of Bohr toposes .

In quantum computing the quantum analog of classical logic gates are called *quantum logic gates*.

added to *S-matrix* a useful historical comment by Ron Maimon (see there for citation)

in order to satisfy links, but maybe really in procrastination of other duties, I wrote something at quantum gravity

]]>added a bit more text to the Idea-section at *Wick rotation* and in particular added cross-links with *Osterwalder-Schrader theorem*.

stub for *confinement*, but nothing much there yet. Just wanted to record the last references there somewhere.

created *worldline formalism* to go with this Physics.SE answer

Prompted by discussion elsewhere, I thought it would be good to have some comments on the $n$Lab on what justifies to speak of “particles” in quantum field theory. So I started at *particle*

a section What is a particle?

a section Particles and non-particles in 3d TQFT

This can clearly be exapanded and and improved a good bit further. But maybe it’s a start.

]]>I needed a table *exceptional spinors and division algebras – table*, and so I have created one and included it into the relevant entries

some basics at *FRW model* (in cosmology)

Since it touches on several of the threads that we happen to have here, hopefully I may be excused for making this somewhat selfish post here.

For various reasons I need to finally upload my notes on “differential cohomology in a cohesive ∞-topos” to the arXiv. Soon. Maybe by next week or so.

It’s not fully finalized, clearly, I could spend ages further polishing this – but then it will probably never be fully finalized, as so many other things.

Anyway, in case anyone here might enjoy eyeballing pieces of it (again), I am keeping the latest version here

]]>I wanted the links to *weak nuclear force* and *strong nuclear force* in various entries to cease appearing grayish and ugly. So I created a minimal entry *nuclear force*.

started *Guillemin-Sternberg geometric quantization conjecture*

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

]]>I have started a category:reference page

such as to be able to point to it for reference, e.g. from Kontsevich 15 etc.

]]>quick note for *5-dimensional Chern-Simons theory*, for the moment just to record some references

added some comments on history to *neutrino*.

added a bunch of pointers to the literature (with brief comments) at *string scattering amplitude*.

Also added a corresponding paragraph at *effective field theory*.

(this is still in reaction to that MO discussion, specifically to the question here)

]]>started *M-theory on G2-manifolds*

For discussion at *geometry of physics* I need a way to point to the concept of “locality” in QFT, so I gave it a small entry: *local quantum field theory*.

I am beginning to give the entry *FQFT* a comprehensive *Exposition and Introduction* section.

So far I have filled some genuine content into the first subsection *Quantum mechanics in Schrödinger picture*.

But I have to quit now. This isn’t even proof-read yet. So don’t look at it unless you feel more in editing-mood than in pure-reading-mood.

]]>stub for *dark matter*

I have added to *cosmic censorship hypothesis* pointer to the recent result (Crisford-Santos 17) showing that it is violated not just in higher dimensions, but also in four spacetime dimensions. And added a minimum of text to go with this. Also cross-linked with *weak gravity conjecture*.

stub for *quantum computation*

needed to be able to point to *duality in physics*, so I created an entry. For the moment just a glorified redirect.

have created *Reissner-Nordström spacetime* with some minimum content.

Nothing non-standard here for the moment, I just wanted the entry to exist in order to be able to point to it. But eventually I’d like to have a linked table that matches extremal black brane solutions to fundamental particles/branes. Not today though.

]]>Does anyone know if there is a definition/construction of spinor bundles which starts with a plain manifold, rather than with a manifold equipped with a metric?

Or to ask an equivalent question: given two Riemannian manifolds with spin structures and a diffeomorphism which preserves the spin structures, is it possible to pull back sections of the spinor bundle from one manifold to the other? And prior to that, what “should” it even mean for a diffeomorphism to preserve the spin structure?

I’d appreciate any pointers to the literature or other sort of input that people here might have.

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