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.
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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
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Source Wigner's theorem, Wikipedia
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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 section
The theorem specifies how physical symmetries such as rotations, translations, and CPT transformations are represented on the Hilbert space of states.
In Branch: Mathematical Physics, Lead
is a cornerstone of the mathematical formulation of quantum mechanics
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