Symmetry¶
Weyl, H. (1952). Symmetry. Princeton University Press.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Equivariance
- Lorentz covariance in special relativity, general covariance in general relativity, and gauge equivariance in gauge field theory all instantiate the same demand: the dynamical relations must commute with the relevant transformation group, a principle Weyl (1952) traces from geometry into physics in his classic study of symmetry.
This sourceCanonical expository treatment tracing symmetry from geometry into physics, covering bilateral, translatory, rotational, ornamental, and crystallographic symmetry and the underlying group-theoretic idea.
- Lorentz covariance in special relativity, general covariance in general relativity, and gauge equivariance in gauge field theory all instantiate the same demand: the dynamical relations must commute with the relevant transformation group, a principle Weyl (1952) traces from geometry into physics in his classic study of symmetry.
- Symmetry
- The continuous case admits Lie-group machinery
This sourceCanonical expository treatment covering discrete and continuous symmetries. Technical Lie-group treatment: Weyl, Gruppentheorie und Quantenmechanik (Leipzig: Hirzel, 1931); English translation The Theory of Groups and Quantum Mechanics (Dover, 1950).
- The continuous case admits Lie-group machinery
- Transformation
- The structural insight is robust: a matrix acting on a vector, a chemical reaction converting reactants to products, a compiler converting source code to machine instructions, a caterpillar metamorphosing into a butterfly, a raw ore being smelted into refined metal, an organization restructuring its governance, and a text being translated into another language all exhibit the same design principle: a rule defines what must be preserved and what may vary, the common structural insight Weyl (1952) elaborates in his classic analysis of symmetry as the unifying language of structure-preserving transformation across mathematics, physics, art, and biology.
This sourceCanonical expository treatment covering discrete and continuous symmetries. Technical Lie-group treatment: Weyl, Gruppentheorie und Quantenmechanik (Leipzig: Hirzel, 1931); English translation The Theory of Groups and Quantum Mechanics (Dover, 1950).
- The structural insight is robust: a matrix acting on a vector, a chemical reaction converting reactants to products, a compiler converting source code to machine instructions, a caterpillar metamorphosing into a butterfly, a raw ore being smelted into refined metal, an organization restructuring its governance, and a text being translated into another language all exhibit the same design principle: a rule defines what must be preserved and what may vary, the common structural insight Weyl (1952) elaborates in his classic analysis of symmetry as the unifying language of structure-preserving transformation across mathematics, physics, art, and biology.
Verification¶
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