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## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• I wanted to be able to point to expectation value without the link being broken. So I added a sentence there, but nothing more for the moment.

• I gave diffiety more of an Idea-section

• New stub Weyl functional calculus redirecting also Weyl quantization. I would like to see ref.

• Lars Hörmander, The weyl calculus of pseudo-differential operators, Comm. Pure Appl. Math. 32, 3, 359–443, May 1979, doi,

but have no access to it (can anybody help?). I also added a sentence at Idea section of functional calculus reflecting that the previous definition there is not fitting functional calculi in the context of quantization, including Weyl’s case. One should do this generality discussion more carefully. the previous definition said that the functional calculus needs to be a homomorphism (from ordinary functions to operator functions). This is true for the functional calculus described in the entry, but not for the wider usage of the phrase like in Weyl functional calculus. Maybe we can resolve this in a better way.

• At field (physics) I am beginning to write an actual introduction to the topic, now in a new section titled “A first idea of quantum fields”.

This means to introduce the concept with precise detail, but in a simple context (trivial and bosonic field bundles over Minkowski spacetime, perturbatively quantized) that allows to get a quick idea of the idea of the concept of (quantum) fields as such, without being distracted by other details.

So far I made it up to the derivation of the EOMs. Discussion of (deformation) quantization is to follow (maybe by tonight, depending on how much trouble I have with the trains) and I plan to sprinkle in the detailed example from scalar field in parallel with the abstract discussion.

• I’ve been entering corrections into the article theory of algebraically closed fields in response to a chat room discussion, but see that the \underbrace command doesn’t work as expected (see the Definition section). What’s the right way to write what is obviously wanted here?

• added the case of dgc superalgebras (here) and expanded the list of examples accordingly

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

• I have expanded the Idea section at state on a star-algebra and added a bunch of references.

The entry used to be called “state on an operator algebra”, but I renamed it (keeping the redirect) because part of the whole point of the definition is that it makes sense without necessarily having represented the “abstract” star-algebra as a C*-algebra of linear operators.

• created evolutionary derivative (what Olver calls the “Fréchet derivative of tuples of differential functions”) with basic definitions and properties

• Gave some content to causal propagator: an Idea-section and the main formulas for the causal propagator on Minkowski spacetime.

• At positive type we have

In denotational semantics, positive types behave well with respect to “call-by-value” and other eager evaluation strategies.

and dually at negative type we have

In denotational semantics, negative types behave well with respect to “call-by-name” and other lazy evaluation strategies.

This doesn’t seem right to me; don’t evaluation strategies belong to operational semantics?

• I want to be adding some details to Cauchy principal value. What’s a good reference? Say for the proof that up to addition of a delta-distribution, $f(x) = pv\left( \frac{1}{x}\right)$ is the unique distributional solution to $x f = 1$?

• I added to field a mention of some other constructive variants of the definition, with a couple more references.

• I made a note of the fact that simple high-school algebra applied to the “Archimdean definition” of pi leads to the Vieta product formula.

• The negation of an apartness relation is an equivalence relation. (The converse of this is equivalent to excluded middle.)

But it seems to me that the converse (“the negation of an equivalence relation is an apartness relation”) only requires de Morgan’s law. If $\approx$ is an equivalence relation, then certainly $\neg\neg(x\approx x)$ and $\neg (x\approx y) \to \neg(y\approx x)$, so the only thing to worry about is comparison. If $\neg (x\approx z)$, then contraposing transitivity gives $\neg (x\approx y \wedge y\approx z)$, which by de Morgan gives $\neg (x\approx y) \vee \neg (y\approx z)$.

• Added to local ring a short remark on that the spectrum of a ring is local if and only if the ring is local.

• added to conservative functor the proposition saying that pullback along strong epis is a conservative functor (if strong epis pull back).

How about the $\infty$-version?

• I have recorded citations for integral representations of Bessel functions (here) needed in the computation of the singular support of the Klein-Gordon propagators (here)