1/N expansion
Let an agent explain the 1/N expansion as a method, its main applications and limits, relay results with attribution to the literature, and route detailed calculations to specialist references.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Idea What the expansion is.
Definition
Definition.
Definition
Definition.
- What is expanded in 1/N, and why does the large N limit simplify a theory? definition
- Is the question about the 1/N expansion or about ordinary perturbation theory? boundary
Organisation
Diagram organisation.
Organisation
Organisation.
- How are diagrams organised by order in 1/N, including the planar limit in gauge theories? definition
- Which entry fits Feynman diagrams? action
Applications Where it is used.
Field theory
Gauge and vector models.
Field
Field.
- How is the expansion used in QCD and in O(N) models, with results attributed? provenance
- Which references are standard? provenance
Other
Statistical mechanics and matrices.
Other
Other.
- How is it used in statistical mechanics, random matrices and holography? provenance
- Which entry fits a specific application? action
Limits Validity and corrections.
Validity
When it works.
Validity
Validity.
- When is the expansion reliable, and how large are corrections for physical N? measurement
- What is proven versus conjectured? boundary
Corrections
Higher orders.
Corrections
Corrections.
- How are higher-order corrections computed and resummed? provenance
- Which entry fits resummation methods? action
Learn History and teaching.
History
History.
History
History.
- How did the method develop from Stanley and t Hooft onward? provenance
- Which entry fits a specific physicist? action
Teach
Teaching.
Teach
Teaching.
- How is the expansion taught in graduate courses, and which texts are standard? provenance
- Which prerequisites are needed? boundary
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.REL
What it is Filled
A perturbative method in theoretical physics in which a theory with N components, colours or flavours is expanded in powers of 1/N, so that the limit of large N becomes tractable and corrections are organised by their order in 1/N; used in quantum chromodynamics, statistical mechanics, matrix models and the study of gauge and string dualities.
Why it exists Filled
Let an agent explain the 1/N expansion as a method, its main applications and limits, relay results with attribution to the literature, and route detailed calculations to specialist references.
Distinguishing features Filled
- Expansion parameter is the inverse number of components
- Large N limit simplifies the theory
- Organises Feynman diagrams by topology in gauge theories
- Applies across field theory, statistical mechanics and matrix models
What robots and AI may and may not do Filled
Must not
- Apply a large N result to small N without noting the size of corrections.
- Confuse vector and matrix large N behaviour.
- Present a conjectured duality or extrapolation as proven.
- Attribute results to researchers who did not obtain them.
Only with a human decision
- Stating that a large N result holds for a physical theory with small N.
May
- Explain the 1/N expansion and where the large N limit simplifies a theory.
- Report results from published work with their stated assumptions.
Moral aspects Filled
- Overstated results mislead students and other researchers.
- Credit for results matters to researchers' careers.
Who is affected
- Researchers and students
- Readers of popular science
Owners Filled
Steward
Nobody owns the method; it belongs to the physics community.
Links to other meta-models Filled
parent
- Q3511310 - registry parent class
related
- perturbative series - an expansion method
- quantum chromodynamics - a main application
- mean-field theory - often the leading order for vector models
- AdS/CFT correspondence - large N is essential to the duality
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.1-n-expansion
- Wikidata: Q951142 (https://www.wikidata.org/wiki/Q951142)
Direct properties not applicable Not applicable
Not applicable
Plane XCT: no invented physical properties.
Recognition optional Filled
- Expansion parameter 1/N with N the number of components or colours
- Leading order often planar or mean-field
- Ordinary coupling-constant perturbation theory is a different expansion
- Not visible; a series in powers of 1/N in equations.
Capabilities and actions required Filled
- explain the idea of large N limits
- describe main applications in field theory and statistical mechanics
- explain planar diagrams and topological organisation
- point to standard references
Hazards and failure modes required Filled
- Applying large N results to small N without checking corrections
- Confusing vector and matrix large N behaviour
- Presenting conjectured dualities as proven
Standards and interfaces required Filled
- No regulation; conventions follow the physics literature
Context of use required Filled
- Making strongly coupled or many-component theories calculable.
- large N vector models such as the O(N) model
- large N gauge theories and the planar limit
- matrix models and random matrices
- large N in condensed matter and spin models
- holographic dualities at large N
Sources Filled
- Wikidata item Q951142: 1/N expansion - identity and sense of the item
- Wikipedia: 1/N expansion - general description of the item
Open questions
- Should vector and matrix large N be separate entries?
- How should standard reviews be linked?
- How should the status of conjectures be recorded?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q951142/spec.json