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    • have created extension of distributions with the statement of the characterization of the space of point-extensions of distributions of finite degree of divergence: here

      This space is what gets identified as the space of renormalization freedom (counter-terms) in the formalization of perturbative renormalization of QFT in the approach of “causal perturbation theory”. Accordingly, the references for the theorem, as far as I am aware, are from the mathematical physics literature, going back to Epstein-Glaser 73. But the statement as such stands independently of its application to QFT, is fairly elementary and clearly of interest in itself. If anyone knows reference in the pure mathematics literature (earlier or independent or with more general statements that easily reduce to this one), please let me know.

    • I created Bishop’s constructive mathematics by moving some material from Errett Bishop and adding some more discussion of what it is and isn’t. Comments and suggestions are very welcome; I’m still trying to figure out the best way to describe the relationship of this theory to other things like topos logic.

    • I added some references to convex space and began a new entry on homomorphism.

      It would be great to see the article on convex spaces continue... it sort of trails off now. I've tried to enlist Tobias Fritz.

    • This is probably a request for Todd!

      Over on colimits for categories of algebras there’s a corollary I really need right now, about Eilerberg-Moore categories being cocomplete, and the remark:

      The hypotheses of the preceding corollary hold when CC is a complete, cocomplete, cartesian closed category and CC is the monad corresponding to a finitary algebraic theory.

      That sounds like exactly what I want, but when I click on finitary algebraic theory I get taken to a page that doesn’t have the definition of “finitary algebraic theory”. I think I know what this means, so I could guess and stick it in, but I think I should let the expert do it.

      Oh, whoops! - as usual, I actually need a multi-sorted generalization. But still it would be nice to have this clarified.

    • I created locally compact groupoid with an attempt at a very general definition, that will be refined to connect with the notion in the literature. In particular, if one has a system of Haar measures on the source (or target) fibres, then this will most likely place further constraints on the topological structure.

    • I have given multigraph its own little entry, so that I can point to it (from discussion of Feynman diagrams).

    • I have given finite graph its own minimum entry, just so as to be able to point to it

    • we didn’t have face

    • I have created an entry-for-inclusion titled

      which is one “Summary box” that means to give a lightning but accurate summary of the origin and meaning of Feynman diagrams in the rigorous description via causal perturbation theory.

      This makes use of a set of nicely done slides in Brouder 10; a citation is contained.

      I am meaning to include this as a Summary-box into relevant entries, such as Feynman diagram and renormalization.

    • I created a new page distributivity of products and colimits, where I recorded what I learned after asking this question: http://nforum.mathforge.org/discussion/6255/commutativity-of-homotopy-sifted-colimits-and-products-in-categories-other-than-sets-or-spaces/

    • I gave product of distributions its own entry. For the moment it just points to the definition in Hörmander’s book.

      This should eventually supercede the section “Multiplication of distributions” at distributions, which I find suboptimal: that section starts very vaguely referring to physics as if the issue only appears there, and it keeps being very vague, with its three sub-subsections being little more than a pointer to one reference by Colombeau.

      I suggest to

      1. remove that whole subsection at distribution and leave just a pointer to product of distributions

      2. move the mentioning of Colombeau’s reference to product of distributions and say how it relates to Hörmander’s definition

      3. remove all vague mentioning of application in physics and instead add a pointer to Wick algebra and microcausal functional, which I will create shortly.

    • started an entry interacting vacuum with some pointers. For instance to

      • Johann Rafelski, Vacuum structure – An Essay, in pages 1-29 of H. Fried, Berndt Müller (eds.) Vacuum Structure in Intense Fields, Plenum Press 1990 (GBooks)

    • I have started spelling out details at quantum master equation, following the rigorous derivation in causal perturbation theory due to Fredenhagen-Rejzner 11b, Rejzner 11.

      So far I have added some backgound infrastructure and then the proof of this theorem ((Rejzner 11, (5.35) - (5.38)):

      Consider an adiabatically switched non-point-interaction action functional in the form of a regular polynomial observable

      S int∈PolyObs(E BV-BRST) reg[[ℏ]], S_{int} \;\in\; PolyObs(E_{\text{BV-BRST}})_{reg}[ [\hbar] ] \,,

      Then the following are equivalent:

      1. The quantum master equation (QME)

        12{S′+S int,S′+S int} 𝒯+iℏΔ BV(S′+S int)=0 \tfrac{1}{2} \{ S' + S_{int}, S' + S_{int} \}_{\mathcal{T}} + i \hbar \Delta_{BV}( S' + S_{int} ) \;=\; 0

        holds on regular polynomial observables.

      2. The perturbative S-matrix on regular polynomial observables is BVBV-closed

        {−S′,𝒮(S int)}=0. \{-S', \mathcal{S}(S_{int})\} = 0 \,.

      Moreover, if these equivalent conditions hold, then the interacting quantum BV-differential is equal, up to a sign, to the sum of the time-ordered antibracket with the total action functional S′+S intS' + S_{int} and iℏi \hbar times the BV-operator:

      ℛ∘{−S′,(−)}∘ℛ −1=−({S′+S int,(−)} 𝒯+iℏΔ BV) \mathcal{R} \circ \{-S',(-)\} \circ \mathcal{R}^{-1} \;=\; - \left( \left\{ S' + S_{int} \,,\, (-) \right\}_{\mathcal{T}} + i \hbar \Delta_{BV} \right)

    • I am starting to write up at BV-operator an account of the rigorous derivation/construction of the BV-operator and the BV quantum master equation in causal perturbation theory, due to Fredenhagen-Rejzner.

      As a first step, the statement and proof of the BV-operator arising as the difference of the plain and time-ordered BV-differential in free field theoy is now here.

    • just out of a whim, I expanded a little the text at Fermat curve

    • Added a link to Informal Notes from the Harvard Fargues-Fontaine Curve seminar at Fargues-Fontaine curve since people like Lurie and Gaitsgory are apt to explain things in a manner that appeals to people at the nlab.

    • Epstein zeta function, just recording the definition and the two classical references by Kronecker and Siegel. Nominally, this is the page 13133 of the nnLab ;)

    • I am starting Wick algebra. So far I have an Idea-section, references, and a discussion of the finite dimensional case, showing how the traditional “normal ordered Wick product” is the Moyal star product of an almost-Kähler vector space.

    • at S-matrix and elsewhere is reference to the “causal order“-relation, the relation saying that for a pair (S 1,S 2)(S_1,S_2) of subsets of a spacetime, S 1S_1 does not intersect the past of S 2S_2, or equivalently that S 2S_2 does not intersect the future of S 1S_1.

      (Following a suggestion by Arnold Neumaier, a neat suggestive notation for this is S 1∨∧S 2S_1 {\vee\!\!\!\wedge} S_2, which I have been implementing now at S-matrix.)

      I am starting to give this concept its own entry, currently titled “causal order”; but what’s good terminology?

      This relation ∨∧{\vee\!\!\!\wedge} is not really an ordering, since it is not transitive. It would seem tempting to say “causal relation”, but googling for this term shows that has an different established meaning.

    • I have added to star product some basic facts, and their proofs, for the case of star products induced from constant rank-2 tensors ω\omega on Euclidean spaces: the definition, proof of the associativity, proof that shifts of ω\omega by symmetric contributions are algebra isomorphisms.

    • I gave Dickey bracket its own entry (just a brief Idea-section and references)

      (the term “Dickey bracket” used to redirect to conserved current, where however it was mentioned only in the references. Now it should be easier to discern what the pointer is pointing to. Of course the entry remains a stub nonetheless.)

    • 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.

    • 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.

    • 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 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.

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