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A new proof of Wigner’s theorem. (English) Zbl 1161.81381
Summary: We present a new, elementary proof for Wigner’s famous unitary-antiunitary theorem.

MSC:
81R15 Operator algebra methods applied to problems in quantum theory
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
46N50 Applications of functional analysis in quantum physics
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[1] Bargmann, V., Note on Wigner’s theorem on symmetry operations, J. math. phys., 5, 862, (1964) · Zbl 0141.23205
[2] Casinelli, G.; Vito, E. de; Lahti, P.; Levrero, A., Symmetry groups in quantum mechanics and the theorem of Wigner on the symmetry transformations, Rev. mat. phys., 8, 921, (1997) · Zbl 0907.46055
[3] Lemont, J.S.; Mendelson, P., The Wigner unitary-antiunitary theorem, Ann. math., 78, 548, (1963) · Zbl 0194.15204
[4] Molnár, L., Wigner’s unitary-antiunitary theorem via Herstein’s theorem on Jordan homeomorphisms, J. nat. geom., 10, 137, (1996) · Zbl 0858.46019
[5] Molnár, L., An algebraic approach to Wigner’s unitary-antiunitary theorem, J. austral. math. soc., 65, 354, (1998) · Zbl 0943.46033
[6] Sharma, C.S.; Almeida, D.L., A direct proof of Wigner’s theorem on maps which preserve transition probabilities between pure states of quantum systems, Ann. phys., 197, 300, (1990) · Zbl 0875.46008
[7] Simon, B., Quantum dynamics: from automorphism to Hamiltonian, (), 327
[8] Rdtz, J., On Wigner’s theorem: remarks, complements,. comments and corrolaries, Aequationes math., 52, 1, (1996)
[9] Varadarajan, V.S., Geometry of quantum theory, (1985), Springer · Zbl 0581.46061
[10] Wigner, E.P., Gruppentheorie and ihre anwendung auf die quantenmechanik der atomspektrum, (1931), Fredrik Vieweg and Sohn New York · JFM 57.1578.03
[11] Wigner, E.P., Group theory: and its application to the quantum mechanics of atomic spectra, (1959), Academic Press · Zbl 0085.37905
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