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created pullback of a distribution, just for completeness
Am starting Green hyperbolic differential equation from
So far I have the definition and then the statement of the first remarkable proposition from this article: here.
I have streamlined the definition-section at microcausal observable a little, giving also polynomial observable its entry. Now there is this chain of inclusions
polynomial local observables ↪ microcausal observables ↪ polynomial observables ↪ observables
I am starting an entry locally covariant perturbative quantum field theory.
[edit: renamed to perturbative algebraic quantum field theory]
So far it contains just an Idea-section and some references to go with it. The same idea I also added as a pointer to the entry quantum field theory.
By this winter I hope to expand the entry to contain a detailed introduction.
In the course of writing that Idea-section, I also created a stub entry causal perturbation theory, and a References-entry The Role of locality in perturbation theory.
Added to Hadamard distribution the standard expression for the standard choice on Minkowski spacetime, as well as statement and proof of its contour integral representation (here)
I have included at geometric quantization the definition of quantum operators associated with a given function on phase space in geometric quantization. Then I decided to split it off to dedicated entry quantum operator.
stub for Stone-von Neumann theorem
I spelled out the elementary definitions, relations and examples at Kähler vector space and Hermitian space.
This started out as a section that I added to Kähler manifold.
Created stable homotopy hypothesis just to record a couple of references.
added some stuff to Lamb shift
also created a stub for radiative correction
at string theory there used to be a stub-section “Fields medal work induced by string theory. I have now expanded that to the following keyword list:
Pure mathematics work which came out of string theory and was awared with a Fields medal includes the following.
Richard Borcherds, 1998
Maxim Kontsevich, 1998
formality theorem and formal deformation quantization via holography of Poisson sigma-model string.
Edward Witten, 1990
knot invariants via WZW model-string/Chern-Simons theory holography;
elliptic genus, Witten genus and rigidity via superstring partition functions;
Grigori Perelman, 2006
added to spectrum with G-action brief paragraphs “Relation to genuine G-spectra”, and “relation to equivariant cohomology”.
Both would deserve to be expanded much more, but it’s a start.
Created phase semantics (of linear logic).
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 created an entry called (infinity,1)-Yoneda extension.
Currently the point of this entry is to present one specific presentation by model category means of what should more abstractly be an (oo,1)-version of the standard Yoneda extension. The statement is (supposed to be) a simple consequence of the proposition recalled at Quillen bifunctor.
I started preparing this entry on my personal web, but then thought that this kind of material should be on the main nLab. Let me know if you disagree.
I put a standout-box cautioning the reader that this is stuff I dreamed up. But even in as far as the statement so far given is right, I would like the entry to be understood as something in search of a bigger and more abstract picture.
Made a stub for admissible rule with a few examples, after seeing the discussion about negation here
I have expanded logical functor by some stuff taken from the Elephant.
In the course of this I have created stubs for cartesian morphism, evaluation map and touched power object.
I have also done some editorial edits to topos (adding subsections and lead-ins)
I started generalized contact geometry since it was in the g+ news.
Created multiplicative disjunction.
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
microformal morphism a la Theodore Voronov.
Stub for Morse potential.
New stub Weyl functional calculus redirecting also Weyl quantization. I would like to see ref.
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.
added a minimum of words at commutative operad (the entry remains a stub)
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
created evolutionary derivative (what Olver calls the “Fréchet derivative of tuples of differential functions”) with basic definitions and properties
I created a stub for hydrogen atom, for the moment just so as to record a reference. In the course of this I ended up touching or creating a few related entries, such as proton, neutron, nucleus (physics), element, periodic table of the elements. But all of these remain stubs at the moment.
created rapidity, just enough to serve as a link from the computation of the singular support of the causal propagator
I gave the definition of symbol order its own entry (an estimate on the decay of the principal symbol of a (psedo-)differential operator that enters the assumptions of the propagation of singularities theorem).
Maybe there is a better name for this? The literature refers to it mostly only in formal notation as “q∈Smρ,δ(X)”.
some minimum at bicharacteristic flow
there was no mention of symplectic struture at cotangent bundle. I have added it: here.
I gave the definition of properly supported pseudo-differential operator its own entry.
I noticed that exceptional Lie algebra was still a missing entry. Just in order to make links work, I created a stub for it. No time for more at the moment.
A while back I had started an overview table propagators - table.
Now I see that a nice table in this spirit, but larger with much more information, has been produced by some M. B. Kocic. I have added pointer to this pdf in a few places.
I gave the entry wave front set more of an Idea-section, and I added pointer to Hörmander’s book.
added to advanced and retarded propagator statement and proof of the expression
ΔR(x,y)=(2π)−(p+1)limε→0+∫e−ikμxμkμkμ+m2−ik0ε/2d4kneeded to be able to point to sign function, so I created it
I have given generalized function its own little entry (it used to be just a redirect to distribution) with some expository words on how to think of and read distributions as “generalized functions”.
Someone started a page called Ahmadnagar. The page is blank otherwise. I tried to find more and googled Ahmadnagar and math and found that in the Ahmadnagar district in India there is a village called Math, with a population of 1851. Strange but it seems true. I have left the nLab page for all to see!
Created a short page for quasi-Borel spaces
I’m pretty sure the definition of a super fiber functor should read ’T = sFinVect’ to agree with the notation earlier in the article rather than the notation in DMOS or Deligne’s paper, where sVect is understood to contain only finite-dimensional super vector spaces. I’ve edited the article to reflect this.
needed to be able to point to direction of a vector.
Added the Frechet space structure on spaces of smooth sections of the smooth vector bundle: here
Created the stub germ of a space, mainly to record the (trivial) insight that the category of germs of spaces is a localization of the category of pointed spaces.
Note that this is not yet a good stub, as it is not interlinked very well. I’m not quite sure where to put it in the table at germ.
I’ve been adding a large number of details to the material Sridhar had started at tripos and also to partial combinatory algebra.
stub at right/left fibration of simplicial spaces to record some references.
Created linear hyperdoctrine.
added the definition to Planck length and to Planck mass and in the course of this cross-linked and slightly expanded correspondingly the entries Compton wavelength and Schwarzschild radius .
created a stub for Dirac current, so far mostly just a pointer to details in A first idea of quantum field theory; and cross-linked with baryogenesis, chiral anomaly, conserved current and Noether’s thoerem
I need to be able to point to linear differential equation, and so I created a minimum entry for this.
Notice that at D-module is missing discussion that these model linear differential equations, but I don’t have the leisure now to do anything about this.
I have brought in some standard stuff to Fourier transform in a new section Over Cartesian spaces. (Superceding the previous section “On the real line”.)
just for completeness and for ease of linking, I gave product of distributions with a smooth function its own entry
I have created an entry-for-inclusion
in order to collect notation and terminology for plane (relativistic) waves (as a glorified “related concepts”-section); and so I am including this now into the relevant entries.
In the course of this I created stubs for speed of light, Compton wavelength and dispersion relation redirecting energy-momentum relation, but no substantial content yet in any of these stub entries.
I’ll go next and harmonize Fourier transform with this.
(Previously I had had the ambition there to stick with the convention where the “2π” is in the exponents, instead of in the global prefactors; but I feel now that this is just too different from established practice, and I’ll change it.)
I keep adding basic material to Fourier transform and copying paragraphs over to the respective stand-alone entries, where missing.
Now I added the example of the Fourier transform of the delta-distribution here and copied it over to Dirac distribution – Fourier transform.
gave wavelength a bare minimum of content
needed to be able to point to wave vector, so I created a bare minimum entry