About Groups for Physics

Groups for Physics connects precise mathematical objects to calculations and interpretations used by graduate students and theoretical physicists.

Read, calculate, and check

Begin with the Atlas to identify a finite group, Lie group, algebra, real form, representation, or map. Follow one of the three learning paths to develop the mathematics. The Physics guides connect that structure to discrete symmetries, gauge fields and matter, symmetry breaking, spinors, CFT, and AdS.

The reference contains 266 mathematical records, 2,998 claims, and 114 source records, including 49 finite groups, 41 Lie groups, 62 representation records, 22 explicit maps and 2 spaces. Fifteen workbenches perform exact calculations within stated input domains. Source locators, convention profiles, downloadable data, and reproducible examples connect the results to their assumptions.

The Standard Model walkthrough joins matter representations and global quotients to local polynomial invariants. Eleven fixed-monomial examples and six field inventories support saved calculations and replay. These tools exclude derivatives, equations of motion, integration by parts, and a complete EFT basis. Coverage states the supported categories and limits.

Evidence and credit

The exposition and software include AI-assisted authoring, source checking, and automated mathematical verification. Independent human expert review is a separately recorded status and remains pending. Read the editorial method, review register, and contributors and credit for the distinctions.

Original articles: CC BY 4.0. Original code: MIT. Reuse terms.

Project information

• Suggest a correction.
• Sources and provenance.
• Roadmap.
• Release history.

The broader QFT context is available at QFT.org.