nLab (original) (raw)
Contents
Contents
Content
Resources
Community
- nForum
* Latest Changes - HowTo
- FAQ
- Contributors?
- Uploaded Files
- Sandbox
- nForum
-
- logic
* internal language
* classical mathematics
* constructive mathematics
* predicative mathematics
* category:foundational axiom - set theory
* structural set theory - category theory
* Categories and Sheaves
* topos theory
* Sheaves in Geometry and Logic - higher category theory
* higher topos theory
* (∞,1)-topos theory
* models for ∞-stack (∞,1)-toposes
* cohomology
* homotopy theory
* stable homotopy theory
* rational homotopy theory
- logic
-
- geometry (general list), topology (general list)
- general topology
- differential topology
- differential geometry
* synthetic differential geometry
* symplectic geometry - algebraic geometry
- noncommutative algebraic geometry
- noncommutative geometry (general flavour)
- higher geometry
physics, mathematical physics, philosophy of physics
Surveys, textbooks and lecture notes
theory (physics), model (physics)
experiment, measurement, computable physics
- mechanics
- field (physics)
- Lagrangian mechanics
* configuration space, state
* action functional, Lagrangian
* covariant phase space, Euler-Lagrange equations - Hamiltonian mechanics
* phase space
* symplectic geometry
* Poisson manifold
* symplectic manifold
* symplectic groupoid
* multisymplectic geometry
* n-symplectic manifold - spacetime
* smooth Lorentzian manifold
* special relativity
* general relativity
* gravity
* supergravity, dilaton gravity
* black hole
- Lagrangian mechanics
- Classical field theory
- Quantum Mechanics
- Quantization
- Quantum Field Theory
- Axiomatizations
* algebraic QFT
* Wightman axioms
* Haag-Kastler axioms
* operator algebra
* local net
* conformal net
* Reeh-Schlieder theorem
* Osterwalder-Schrader theorem
* PCT theorem
* Bisognano-Wichmann theorem
* modular theory
* spin-statistics theorem
* boson, fermion
* functorial QFT
* cobordism
* (∞,n)-category of cobordisms
* cobordism hypothesis-theorem
* extended topological quantum field theory - Tools
* perturbative quantum field theory, vacuum
* effective quantum field theory
* renormalization
* BV-BRST formalism
* geometric ∞-function theory - particle physics
* phenomenology
* models
* standard model of particle physics
* fields and quanta
* Grand Unified Theories, MSSM
* scattering amplitude
* on-shell recursion, KLT relations - Structural phenomena
* universality class
* quantum anomaly
* Green-Schwarz mechanism
* instanton
* spontaneously broken symmetry
* Kaluza-Klein mechanism
* integrable systems
* holonomic quantum fields - Types of quantum field thories
* TQFT
* 2d TQFT
* Dijkgraaf-Witten theory
* Chern-Simons theory
* TCFT
* A-model, B-model
* homological mirror symmetry
* QFT with defects
* conformal field theory
* (1,1)-dimensional Euclidean field theories and K-theory
* (2,1)-dimensional Euclidean field theory and elliptic cohomology
* CFT
* WZW model
* 6d (2,0)-supersymmetric QFT
* gauge theory
* field strength
* gauge group, gauge transformation, gauge fixing
* examples
* electromagnetic field, QED
* electric charge
* magnetic charge
* Yang-Mills field, QCD
* Yang-Mills theory
* spinors in Yang-Mills theory
* topological Yang-Mills theory
* Kalb-Ramond field
* supergravity C-field
* RR field
* first-order formulation of gravity
* general covariance
* supergravity
* D'Auria-Fre formulation of supergravity
* gravity as a BF-theory
* sigma-model
* particle, relativistic particle, fundamental particle, spinning particle, superparticle
* string, spinning string, superstring
* membrane
* AKSZ theory
- Axiomatizations
- String Theory
- number theory and physics
This is a wiki for collaborative work on Mathematics, Physics, and Philosophy — especially (but far from exclusively) from the higher structures point of view: with a sympathy towards the tools and perspectives of homotopy theory/algebraic topology, homotopy type theory, higher category theory and higher categorical algebra.
Contents
- Purpose
- nForum, discussion, comments, and questions
- Contributing to the nnLab
- Viewing and editing the nnLab
- Making use of material from the nnLab
- Installation
- Contact
- Steering Committee
Purpose
The nLab records and explores a wide range of mathematics, physics, and philosophy. Along with work of an expository nature, original material can be found in abundance, as can notes from evolving research. Where mathematics, physics, and philosophy arise in other fields, computer science and linguistics for example, the nLab explores these too.
If you take a little time to find something in the literature, or to work through a proof or example, or to find an intuitive or new way to think about something, add a note on it to the nLab! Others will benefit, and you may well find that it proves useful to you too.
A fundamental idea behind the nLab is that the linking between pages of a wiki is a profound way to record knowledge, placing it in a rich context.
For more, see also Urs Schreiber‘s thoughts at What is… the nLab?.
nForum, discussion, comments, and questions
Most nLab pages have a corresponding discussion thread at the nForum, linked to in the menus at the top and bottom of the page. For all but the most trivial edits (correcting spelling or punctuation, etc), we ask that you announce your changes at the nForum using the box at the bottom of the edit page. Typically this would be a short note summarising what you have done, but it can also include what you plan to do, or what you would like others to do! See Welcome to the nForum for more on the nForum.
If you have any questions about an nLab page, or would like to discuss or make a comment upon something in it, whether because you feel that something is wrong or missing or for any other reason, you are encouraged and very welcome to use the nForum discussion thread for the page for this purpose too. If the discussion thread does not yet exist, feel free to create it manually: use the ‘nLab - Latest changes’ category, and give it the same title (case-sensitive!) as the nLab page.
The pages of the nLab have almost always been edited by several people. In almost all cases, we recommend that you use the nForum rather than contact an author of an edit directly, but if you do have a reason to do this, the history of edits to the page with the details of who made them can be found by clicking on ‘History’ at the bottom of the page.
Contributing to the nnLab
If after looking around for a while you feel like contributing yourself, you are very welcome to do so! See below for more on how to actually edit, as well as the HowTo.
If you make any edits to the nLab, please follow the guidelines for announcing your changes at the nForum given above. If you are unsure whether what you would like to contribute is appropriate, please ask at the nForum before making the edit.
Viewing and editing the nnLab
The nLab should be viewable and editable in any modern web browser on any device. For technical reasons, browsers which are able to render MathML, such as Firefox, may render very large pages quicker than other browsers, but these pages are few and far between, and most people will be able to use the browser of their choice.
Editing the nLab these days can be done more or less as in LaTeX. Macros are not currently available, but mathematics can be entered within dollar signs as usual, theorem environments, sections and tables of contents can be defined as in LaTeX, commutative diagrams and figures can be created in Tikz or XyMatrix, and so on. For simple formatting, such as italics, and for some other things such as tables, Markdown is used.
See the HowTo for more on editing the nLab.
Making use of material from the nnLab
One goal of the nnLab is to help make information widely available and usefully related to other information. In this users and contributors are expected to follow traditional academic practice:
- Using and distributing content obtained from the nnLab is free and encouraged if you acknowledge the source, as usual in academia.
(There is currently no consensus on a more formal license statement, but if it matters check if relevant individual contributors state such on their nnLab homepages.)
If you cite a page you may want to point to a specific version of it, because nnLab pages can change. You can find a list of all the versions of a page by clicking on the History link at the bottom of the page itself. - Conversely, any content contributed to the nnLab is publicly available and you should be aware that others may use your contributions (whatever you decide to do with their content elsewhere) and indeed may edit them. In the first case you trust that users will cite your contributions properly, in the second that they will respect and only improve on them. At the same time, you are expected to properly acknowledge sources of information for material entered into the nnLab.
Usually this works well. If there is need for discussion, the nForum is the forum to turn to. If serious problems arise, the steering committee might intervene.
Installation
The domain ncatlab.org
is owned by Urs Schreiber.
The nnLab server is currently hosted at Carnegie Mellon University, kindly provided by Steve Awodey.
The nLab’s software and technical administrative matters are in the hands of the nLab’s technical board.
Much of the software behind the nLab has been written especially for the nLab: the latest source can be found at GitHub. It was originally an instance of Instiki.
The nnLab page style is due to Jake Bian, originating with his Kan browser extension
The nnLab logo is due to David Roberts, inspired by Matisse’s painting La Gerbe. Besides being an inside reference to higher structures known as gerbes, the logo represents maybe computational trinitarianism or the progression of modalities or generally the unity of diverse mathematical phenomena revealed by the nPOV.
The default venue for all communication regarding the nLab is the nForum. When posting there you get to choose a “category”-label for your message:
- Latest edit logs are to be posted under Latest changes.
- Organizational matters (such as concerning user accounts) are best posted under nLab Organisation.
- Technical bug reports or software feature requests are best raised in nLab Technical Matters
or directly on github.com/ncatlab/nlab/issues.
Please do not try to contact the technical team on matters that are not purely technical: Policy decisions are made by the active nLab community or, if all fails, by the Steering Committee.
Steering Committee
The nnLab is a community undertaking. But for all matters that do require that the nnLab is represented to the outside by an official decision-taking body, we have the steering committee. Nobody “is in charge of the nnLab”. But the steering committee is the closest approximation to a body being in charge that we have.
Last revised on March 30, 2024 at 02:03:46. See the history of this page for a list of all contributions to it.