Note on Wigner's Theorem on Symmetry Operations

1964/07/01 by V. Bargmann · 6 citations
Physics and Astronomy · Chemistry · Computer Science · Mathematics · #Quantum Mechanics and Applications #Molecular spectroscopy and chirality #Quantum Information and Cryptography #Unitary state #Symmetry (geometry) #Exposition (narrative) #Mathematics #Unitary transformation #Transformation (genetics) #Mathematical physics #Quantum #Pure mathematics #Theoretical physics #Algebra over a field #Quantum mechanics #Physics #Law #Geometry

paper · doi:10.1063/1.1704188

openalex publication_date 1964/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/07

Abstract

Wigner's theorem states that a symmetry operation of a quantum system is induced by a unitary or an anti-unitary transformation. This note presents a detailed proof which closely follows Wigner's original exposition.

Citations

• Foundations of Quaternion Quantum Mechanics

Cited by

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• Events in a noncommutative space-time
• Normalizability analysis of the generalized quantum electrodynamics from the causal point of view
• Invariants in Co-polar Interferometry: an Abelian Gauge Theory
• An elementary proof for the non-bijective version of Wigner's theorem
• Wigner's theorem [wikipedia]