Wigner's Theorem states that every symmetry of a quantum-mechanical system, meaning every transformation that preserves the probabilities predicted by the theory, can be represented on the system's Hilbert space by an operator that is either unitary and linear or anti-unitary and antilinear. Named for Eugene Wigner, it is a foundational result of the mathematical formulation of quantum mechanics, justifying the standard representation of symmetries by unitary operators.
Facts
StatementThe theorem specifies how physical symmetries such as rotations, translations, and CPT transformations are represented on the Hilbert space of states. 2 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Wigner's theorem (Wikipedia)
Wikipedia Wigner's theorem lead paragraph (w-bbfill-psymath4-0926)Quote, Wikipedia Wigner's theorem lead paragraph (w-bbfill-psymath4-0926)
proved by Eugene Wigner in 1931
2. Wigner's theorem, Wikipedia
Lead sectionQuote, Lead section
The theorem specifies how physical symmetries such as rotations, translations, and CPT transformations are represented on the Hilbert space of states.
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