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Adding reference
Anonymouse
added pointer to:
Zhiyuan Wang, Kaden R. A. Hazzard: Particle exchange statistics beyond fermions and bosons, Nature 637 (2025) 314-318 [arXiv:2308.05203, doi:10.1038/s41586-024-08262-7]
Zhiyuan Wang: Parastatistics and a secret communication challenge [arXov:2412.13360]
making this a stand-alone entry (“2-sphere” used to redirect to sphere, which however ended up being about n-spheres in generality)
but it is just a stub for the time being. Mainly I was looking to make a home for these references on ΩS2:
in relation to braid groups:
and regarded as a classifying space, ΩS2≃BΩ2S2 (for “line” bundles):
Jack Morava: A homotopy-theoretic context for CKM/Birkhoff renormalization [arXiv:2307.10148, spire:2678618]
Jack Morava: Some very low-dimensional algebraic topology [arXiv:2411.15885]
created a bare minimum at light-cone gauge quantization, just so as to be able to sensibly link to it from elsewhere
started Thom space
added pointer to these two recent references, identifying further L∞-algebra structure in Feynman amplitudes/S-matrices of perturbative quantum field theory:
Markus B. Fröb, Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories (arXiv:1803.10235)
Alex Arvanitakis, The L∞-algebra of the S-matrix (arXiv:1903.05643)
I am starting higher spin gauge theory
Added link to finite étale morphism of anabelioids.
Started the stub for semilinear map. More to come.
added these two quotes:
Yang wrote in C. N. Yang, Selected papers, 1945-1980, with commentary, W. H. Freeman and Company, San Francisco, 1983, on p. 567:
In 1975, impressed with the fact that gauge fields are connections on fiber bundles, I drove to the house of S. S. Chern in El Cerrito, near Berkeley… I said I found it amazing that gauge theory are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added: “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.
Yang expanded on this passage in an interview recorded as: C. N. Yang and contemporary mathematics, chapter in: Robin Wilson, Jeremy Gray (eds.), Mathematical Conversations: Selections from The Mathematical Intelligencer, Springer 2001, on p. 72 (GoogleBooks):
But it was not just joy. There was something more, something deeper: After all, what could be more mysterious, what could be more awe-inspiring, than to find that the structure of the physical world is intimately tied to the deep mathematical concepts, concepts which were developed out of considerations rooted only in logic and the beauty of form?
Started an entry in “category:motivation” on fiber bundles in physics.
(prompted by this Physics.SE question)
I removed some spam on category theory.
recording the 1-categorical equivalence Ho(CombModCat)≃Ho(PresentableDerivators) obtained from Renaudin06
Created stub. This used to redirect to codomain fibration, but I think that’s wrong.
I have expanded various sections at disjoint coproduct. In particular towards the end is now a mentioning of the fact that in a positive category morphisms into a disjoint coproduct are given by factoring disjoint summands of the domain through the canonical inclusions.
Also,I made positive category and variants redirect to extensive category.
a bare list of references, to be !include-ed into lists of references of relevant entries (such as 2d CFT, 2d SCFT, conformal cobordism category, modular functor and maybe elsewhere)
at DHR superselection theory I have added the argument (here) for why every DHR representation indeed comes from a net-endomorphism, assuming Haag duality and that the net takes values in vN algebras.
added to equivariant K-theory comments on the relation to the operator K-theory of crossed product algebras and to the ordinary K-theory of homotopy quotient spaces (Borel constructions). Also added a bunch of references.
(Also finally added references to Green and Julg at Green-Julg theorem).
This all deserves to be prettified further, but I have to quit now.
Began Freyd cover. What’s it for?
Added to Hopf monad the Bruguières-Lack-Virelizier definition and some properties.
edited reflective subcategory and expanded a bit the beginning
stub for braid group statistics (again, for the moment mainly in order to record a reference)