Not signed in (Sign In)

A discussion forum about contributions to the nLab wiki and related areas of mathematics, physics, and philosophy.

Want to take part in these discussions? Sign in if you have an account, or apply for one below

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory kan lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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

If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

- Discussion Type
- discussion topicKMS state
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 9th 2018

discovered by chance that we have this stub entry here. Added some lines of an Idea-section and cross-linked with

*thermal quantum field theory*and*Wick rotation*

- Discussion Type
- discussion topicG-structure
- Category Latest Changes
- Started by zskoda
- Comments 14
- Last comment by Urs
- Last Active Nov 9th 2018

I do not understand the entry G-structure. G-structure is, as usual, defined there as the principal $G$-subbundle of the frame bundle which is a $GL(n)$-principal bundle. I guess this makes sense for equivariant injections along any Lie group homomorphism $G\to GL(n)$. The entry says something about spin structure, warning that the group $Spin(n)$ is not a subgroup of $GL(n)$. So what is meant ? The total space of a subbundle is a subspace at least. Does this mean that I consider the frame bundle first as a (non-principal) $Spin(n)$-bundle by pulling back along a fixed noninjective map $Spin(n)\to GL(n)$ and then I restrict to a chosen subspace on which the induced action of Spin group is principal ?

- Discussion Type
- discussion topiccorrelator
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 9th 2018

- Discussion Type
- discussion topiccorrelator as differential form on configuration space of points
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 9th 2018

I was thinking/hoping now that a general approach to perturbative QFT should exist, where all Feynman amplitudes are regarded not as singular distributions on $M^n$, but as smooth differential forms on the FM-compactification of the configuration space of $n$ points. Mentioning this hunch to Igor Khavkine, he immediately recalled having heard Marko Berghoff speak about developing just that in his thesis Berghoff 14.

- Discussion Type
- discussion topicJan Raphael Høegh-Krohn
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 9th 2018

brief category:people-entry for hyperlinking references at

*thermal field theory*

- Discussion Type
- discussion topicspacetime support
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 9th 2018

- Discussion Type
- discussion topicValeri Frolov
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 8th 2018

- Discussion Type
- discussion topicconcordance
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 8th 2018

made more explicit (here) the back-link to

*topological vector bundle*for classical concordance for topological vector bundles

- Discussion Type
- discussion topicInitiality Project - Partial Interpretation
- Category Latest Changes
- Started by Mike Shulman
- Comments 9
- Last comment by Mike Shulman
- Last Active Nov 8th 2018

- Discussion Type
- discussion topicMarija Zamaklar
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 8th 2018

brief category:people-entry for hyperlinking references at

*Euclidean field theory*and*lattice gauge theory*

- Discussion Type
- discussion topicprimitive recursive arithmetic
- Category Latest Changes
- Started by David_Corfield
- Comments 3
- Last comment by Todd_Trimble
- Last Active Nov 7th 2018

- Discussion Type
- discussion topicRobert Schrader
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 7th 2018

- Discussion Type
- discussion topicDialectica interpretation
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Nov 7th 2018

Made a start. I linked to lenses (in computer science) since according to the penultimate entry there, Gödel provided the first instance. I guess the connection goes via games, linear logic, etc.

Anyway, to be expanded by someone who knows about these things.

- Discussion Type
- discussion topicNicolaas de Bruijn
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Nov 7th 2018

- Discussion Type
- discussion topicresolution of singularities
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by DavidRoberts
- Last Active Nov 6th 2018

added pointer to

Heisuke Hironaka,

*Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I*, Annals of Mathematics Second Series, Vol. 79, No. 1 (Jan., 1964), pp. 109-203 (95 pages) (jstor:1970486)Michael Atiyah,

*Resolution of singularities and Division of Distributions*, Communications in Pure and Applied Mathematics, vol. XXIII, 145-150 (1970)

with some comment

- Discussion Type
- discussion topicinter-universal Teichmüller theory
- Category Latest Changes
- Started by Urs
- Comments 102
- Last comment by DavidRoberts
- Last Active Nov 6th 2018

added to

*inter-universal Teichmüller theory*a pointer to the recent note- Yamashita,
*FAQ on ‘Inter-Universality’*(pdf)

(Though after reading I am not sure if that note helps so much.)

- Yamashita,

- Discussion Type
- discussion topicsuspension spectrum
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 6th 2018

stub for suspension spectrum

- Discussion Type
- discussion topicIntroduction to Cobordism and Complex Oriented Cohomology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 6th 2018

- Discussion Type
- discussion topiccombinatorial model category
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by nLab edit announcer
- Last Active Nov 5th 2018

added to combinatorial model category a reference (here) discussing that using a funny set-theoretic assumption about large cardinals, every cofibrantly generated mod cat is Quillen equivalent to a combinatorial one.

Weird that set-theory...

- Discussion Type
- discussion topicCisinski model structure
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by nLab edit announcer
- Last Active Nov 5th 2018

created Cisinski model structure

- Discussion Type
- discussion topicgraph complex
- Category Latest Changes
- Started by zskoda
- Comments 22
- Last comment by Urs
- Last Active Nov 5th 2018

A stub (now just recording references and links) graph homology with redirect and section open also for graph cohomology. Related person entry Andrey Lazarev and more references at operad. In operadic literature there is a terminology Feynman transform.

- Discussion Type
- discussion topicwonderful compactification
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 5th 2018

a stub, just to finally make that link at

*compactification*work

- Discussion Type
- discussion topicChristoph Bergbauer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 5th 2018

brief category:people-entry for hyperlinking references at

*Feynman amplitude on compactified configuration space of points*

- Discussion Type
- discussion topicCorrado de Concini
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 5th 2018

brief category:people-entry for hyperlinking references at

*wonderful compactification*and at*Fulton-MacPherson compactification*

- Discussion Type
- discussion topicHeisuke Hironaka
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 5th 2018

brief category:people-entry for hyperlinking references at

*resolution of singularities*

- Discussion Type
- discussion topic2d SCFT
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 5th 2018

added pointer to this article on the arXiv today:

A hint for a relation to tmf, vaguely in line with the lift of the Witten genus to the string orientation of tmf:

- Davide Gaiotto, Theo Johnson-Freyd,
*Holomorphic SCFTs with small index*(arXiv:1811.00589)

- Davide Gaiotto, Theo Johnson-Freyd,

- Discussion Type
- discussion topicChern-Simons theory
- Category Latest Changes
- Started by Bruce
- Comments 40
- Last comment by Urs
- Last Active Nov 5th 2018

- I started an entry on Chern-Simons theory, after having been inspired by news that Witten has thought up a new Morse theory approach to the defining the path integral nonperturbatively (see Not Even Wrong), and Urs' encouragement. There is so much material on Chern-Simons theory, and I am only familiar with a small portion of it, that having to do with "extended topological quantum field theory".

- Discussion Type
- discussion topicChern-Simons propagator
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 5th 2018

- Discussion Type
- discussion topicMarko Berghoff
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 5th 2018

brief category:people-entry for hyperlinking references at

*Feynman amplitudes on compactified configuration spaces of points*and at*wonderful compactification*

- Discussion Type
- discussion topicrenormalization
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Nov 5th 2018

at

*renormalization*I made the Definition-section have three different subsections, a new one of which is now*Definition – Of theories in BV-CS form*on Kevin Costello’s apprach. On the other hand, so far this contains mostly just a pointer to his article.