Sigma model
field theory of a point particle confined to move on a fixed manifold
In physics, a sigma model is a field theory that describes the field as a point particle confined to move on a fixed manifold. This manifold can be taken to be any Riemannian manifold, although it is most commonly taken to be either a Lie group or a symmetric space. The model may or may not be quantized. An example of the non-quantized version is the Skyrme model; it cannot be quantized due to non-linearities of power greater than 4. In general, sigma models admit (classical) topological soliton solutions, for example, the skyrmion for the Skyrme model. When the sigma field is coupled to a gauge field, the resulting model is described by Ginzburg–Landau theory. This article is primarily devoted to the classical field theory of the sigma model; the corresponding quantized theory is presented in the article titled "non-linear sigma model".
Overview
The name has roots in particle physics, where a sigma model describes the interactions of pions. Unfortunately, the "sigma meson" is not described by the sigma-model, but only a component of it.
The sigma model was introduced by Gell-Mann & Lévy (1960, section 5); the name σ-model comes from a field in their model corresponding to a spinless meson called σ, a scalar meson introduced earlier by Julian Schwinger.
This brief starts where responsible research should: with the source description of “Sigma model” as field theory of a point particle confined to move on a fixed manifold. Everything that follows is an evidence route, not borrowed authority.
Why this record matters
The subject matters to the general reference register because the source frames it as field theory of a point particle confined to move on a fixed manifold. Its deeper value depends on whether names, dates, institutions and citations support that framing.
Vocabulary and entity names are the principal evidence signals here, because they determine the precision of every later search. The source revision retrieved here is dated Jan 12, 2026. The linked authority identifier is Q7512415. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1960.
Overview language is designed for orientation and should not be treated as a substitute for the evidence cited beneath it. The source lead contains qualifying language; that uncertainty should survive quotation, summary and reuse. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Sigma model”, its source revision and the description used here.
- Expand the search: follow Sigma model primary sources, Sigma model archive and Sigma research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Sigma model”?
- Which cited source is closest to the event, object or claim?
- What terminology or title could unlock a more precise catalogue search?
Search terms from this dossier
This entry incorporates text from “Sigma model” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.