Wigner's theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Wigner's theorem" in English language version.

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Here the possibility of superselection rules is ignored. It may be the case that a system cannot be prepared in specific states. For instance, superposition of states with different spin is generally believed impossible. Likewise, states being superpositions of states with different charge are considered impossible. Minor complications due to those issues are treated in Bogoliubov, Logunov & Todorov (1975) Bogoliubov, N. N.; Logunov, A.A.; Todorov, I. T. (1975). Introduction to axiomatic quantum field theory. Mathematical Physics Monograph Series. Vol. 18. Translated to English by Stephan A. Fulling and Ludmila G. Popova. New York: Benjamin. ASIN B000IM4HLS.
Wigner 1931, pp. 251–254 (in German),
Wigner 1959, pp. 233–236 (English translation). Wigner, E. P. (1931). Gruppentheorie und ihre Anwendung auf die Quanten mechanik der Atomspektren (in German). Braunschweig, Germany: Friedrich Vieweg und Sohn. pp. 251–254. ASIN B000K1MPEI. Wigner, E. P. (1959). Group Theory and its Application to the Quantum Mechanics of Atomic Spectra. translation from German by J. J. Griffin. New York: Academic Press. pp. 233–236. ISBN 978-0-1275-0550-3.

archive.org

There is an exception to this. If a superselection rule is in effect, then the phase may depend on in which sector of $H$ the element $\Psi$ resides, see Weinberg 2002, p. 53 Weinberg, S. (2002), The Quantum Theory of Fields, vol. I, Cambridge University Press, ISBN 978-0-521-55001-7
Again there is an exception. If a superselection rule is in effect, then the phase may depend on in which sector of $H$ $h$ resides on which the operators act, see Weinberg 2002, p. 53 Weinberg, S. (2002), The Quantum Theory of Fields, vol. I, Cambridge University Press, ISBN 978-0-521-55001-7
Weinberg 2002, p. 49. Weinberg, S. (2002), The Quantum Theory of Fields, vol. I, Cambridge University Press, ISBN 978-0-521-55001-7
Weinberg 2002, p. 50 Weinberg, S. (2002), The Quantum Theory of Fields, vol. I, Cambridge University Press, ISBN 978-0-521-55001-7
Weinberg 2002, p. 51 Weinberg, S. (2002), The Quantum Theory of Fields, vol. I, Cambridge University Press, ISBN 978-0-521-55001-7
Weinberg 2002, p. 82 Weinberg, S. (2002), The Quantum Theory of Fields, vol. I, Cambridge University Press, ISBN 978-0-521-55001-7
Weinberg 2002, Appendix B, Chapter 2 Weinberg, S. (2002), The Quantum Theory of Fields, vol. I, Cambridge University Press, ISBN 978-0-521-55001-7
Weinberg 2002, Section 2.7. Weinberg, S. (2002), The Quantum Theory of Fields, vol. I, Cambridge University Press, ISBN 978-0-521-55001-7

arxiv.org

Simon et al. 2008 Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.; Hamhalter, J. (2008). "Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics". Phys. Lett. A. 372 (46): 6847–6852. arXiv:0808.0779. Bibcode:2008PhLA..372.6847S. doi:10.1016/j.physleta.2008.09.052. S2CID 53858196.
Straumann 2014 Straumann, N. (2014). "Unitary Representations of the inhomogeneous Lorentz Group and their Significance in Quantum Physics". In A. Ashtekar; V. Petkov (eds.). Springer Handbook of Spacetime. Springer Handbooks. pp. 265–278. arXiv:0809.4942. Bibcode:2014shst.book..265S. CiteSeerX 10.1.1.312.401. doi:10.1007/978-3-642-41992-8_14. ISBN 978-3-642-41991-1. S2CID 18493194.
Moretti, Valter (October 2016). "Mathematical Foundations of Quantum Mechanics: An Advanced Short Course". International Journal of Geometric Methods in Modern Physics. 13 (Supp. 1): 1630011–1630843. arXiv:1508.06951. Bibcode:2016IJGMM..1330011M. doi:10.1142/S0219887816300117.

degruyter.com

Simon, Barry (8 March 2015). "Quantum Dynamics: From Automorphism to Hamiltonian". Studies in Mathematical Physics: Essays in Honor of Valentine Bargmann. Princeton University Press. pp. 327–350. doi:10.1515/9781400868940-016. ISBN 978-1-4008-6894-0 – via www.degruyter.com.

doi.org

Seitz, Vogt & Weinberg 2000 Seitz, F.; Vogt, E.; Weinberg, A. M. (2000). "Eugene Paul Wigner. 17 November 1902 -- 1 January 1995". Biogr. Mem. Fellows R. Soc. 46: 577–592. doi:10.1098/rsbm.1999.0102.
Simon et al. 2008 Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.; Hamhalter, J. (2008). "Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics". Phys. Lett. A. 372 (46): 6847–6852. arXiv:0808.0779. Bibcode:2008PhLA..372.6847S. doi:10.1016/j.physleta.2008.09.052. S2CID 53858196.
Page 1987. Page, Don N. (1987). "Geometrical description of Berry's phase". Physical Review A. 36 (7). American Physical Society (APS): 3479–3481. Bibcode:1987PhRvA..36.3479P. doi:10.1103/physreva.36.3479. ISSN 0556-2791. PMID 9899276.
Bargmann 1964. Bargmann, V. (1964). "Note on Wigner's Theorem on Symmetry Operations". Journal of Mathematical Physics. 5 (7). AIP Publishing: 862–868. Bibcode:1964JMP.....5..862B. doi:10.1063/1.1704188. ISSN 0022-2488.
Faure 2002 Faure, Claude-Alain (2002). "An Elementary Proof of the Fundamental Theorem of Projective Geometry". Geometriae Dedicata. 90: 145–151. doi:10.1023/A:1014933313332. S2CID 115770315.
Straumann 2014 Straumann, N. (2014). "Unitary Representations of the inhomogeneous Lorentz Group and their Significance in Quantum Physics". In A. Ashtekar; V. Petkov (eds.). Springer Handbook of Spacetime. Springer Handbooks. pp. 265–278. arXiv:0809.4942. Bibcode:2014shst.book..265S. CiteSeerX 10.1.1.312.401. doi:10.1007/978-3-642-41992-8_14. ISBN 978-3-642-41991-1. S2CID 18493194.
Kadison, Richard V. (1 February 1965). "Transformations of states in operator theory and dynamics". Topology. 3: 177–198. doi:10.1016/0040-9383(65)90075-3. ISSN 0040-9383.
Simon, Barry (8 March 2015). "Quantum Dynamics: From Automorphism to Hamiltonian". Studies in Mathematical Physics: Essays in Honor of Valentine Bargmann. Princeton University Press. pp. 327–350. doi:10.1515/9781400868940-016. ISBN 978-1-4008-6894-0 – via www.degruyter.com.
Moretti, Valter (October 2016). "Mathematical Foundations of Quantum Mechanics: An Advanced Short Course". International Journal of Geometric Methods in Modern Physics. 13 (Supp. 1): 1630011–1630843. arXiv:1508.06951. Bibcode:2016IJGMM..1330011M. doi:10.1142/S0219887816300117.

harvard.edu

ui.adsabs.harvard.edu

Simon et al. 2008 Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.; Hamhalter, J. (2008). "Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics". Phys. Lett. A. 372 (46): 6847–6852. arXiv:0808.0779. Bibcode:2008PhLA..372.6847S. doi:10.1016/j.physleta.2008.09.052. S2CID 53858196.
Page 1987. Page, Don N. (1987). "Geometrical description of Berry's phase". Physical Review A. 36 (7). American Physical Society (APS): 3479–3481. Bibcode:1987PhRvA..36.3479P. doi:10.1103/physreva.36.3479. ISSN 0556-2791. PMID 9899276.
Bargmann 1964. Bargmann, V. (1964). "Note on Wigner's Theorem on Symmetry Operations". Journal of Mathematical Physics. 5 (7). AIP Publishing: 862–868. Bibcode:1964JMP.....5..862B. doi:10.1063/1.1704188. ISSN 0022-2488.
Straumann 2014 Straumann, N. (2014). "Unitary Representations of the inhomogeneous Lorentz Group and their Significance in Quantum Physics". In A. Ashtekar; V. Petkov (eds.). Springer Handbook of Spacetime. Springer Handbooks. pp. 265–278. arXiv:0809.4942. Bibcode:2014shst.book..265S. CiteSeerX 10.1.1.312.401. doi:10.1007/978-3-642-41992-8_14. ISBN 978-3-642-41991-1. S2CID 18493194.
Moretti, Valter (October 2016). "Mathematical Foundations of Quantum Mechanics: An Advanced Short Course". International Journal of Geometric Methods in Modern Physics. 13 (Supp. 1): 1630011–1630843. arXiv:1508.06951. Bibcode:2016IJGMM..1330011M. doi:10.1142/S0219887816300117.

nih.gov

pubmed.ncbi.nlm.nih.gov

Page 1987. Page, Don N. (1987). "Geometrical description of Berry's phase". Physical Review A. 36 (7). American Physical Society (APS): 3479–3481. Bibcode:1987PhRvA..36.3479P. doi:10.1103/physreva.36.3479. ISSN 0556-2791. PMID 9899276.

psu.edu

citeseerx.ist.psu.edu

Straumann 2014 Straumann, N. (2014). "Unitary Representations of the inhomogeneous Lorentz Group and their Significance in Quantum Physics". In A. Ashtekar; V. Petkov (eds.). Springer Handbook of Spacetime. Springer Handbooks. pp. 265–278. arXiv:0809.4942. Bibcode:2014shst.book..265S. CiteSeerX 10.1.1.312.401. doi:10.1007/978-3-642-41992-8_14. ISBN 978-3-642-41991-1. S2CID 18493194.

semanticscholar.org

api.semanticscholar.org

Simon et al. 2008 Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.; Hamhalter, J. (2008). "Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics". Phys. Lett. A. 372 (46): 6847–6852. arXiv:0808.0779. Bibcode:2008PhLA..372.6847S. doi:10.1016/j.physleta.2008.09.052. S2CID 53858196.
Faure 2002 Faure, Claude-Alain (2002). "An Elementary Proof of the Fundamental Theorem of Projective Geometry". Geometriae Dedicata. 90: 145–151. doi:10.1023/A:1014933313332. S2CID 115770315.
Straumann 2014 Straumann, N. (2014). "Unitary Representations of the inhomogeneous Lorentz Group and their Significance in Quantum Physics". In A. Ashtekar; V. Petkov (eds.). Springer Handbook of Spacetime. Springer Handbooks. pp. 265–278. arXiv:0809.4942. Bibcode:2014shst.book..265S. CiteSeerX 10.1.1.312.401. doi:10.1007/978-3-642-41992-8_14. ISBN 978-3-642-41991-1. S2CID 18493194.

stackexchange.com

physics.stackexchange.com

"(Coming from Wigner's Theorem): What is a Symmetry in QFT?". Physics Stack Exchange. Retrieved 2023-10-18.

worldcat.org

Page 1987. Page, Don N. (1987). "Geometrical description of Berry's phase". Physical Review A. 36 (7). American Physical Society (APS): 3479–3481. Bibcode:1987PhRvA..36.3479P. doi:10.1103/physreva.36.3479. ISSN 0556-2791. PMID 9899276.
Bargmann 1964. Bargmann, V. (1964). "Note on Wigner's Theorem on Symmetry Operations". Journal of Mathematical Physics. 5 (7). AIP Publishing: 862–868. Bibcode:1964JMP.....5..862B. doi:10.1063/1.1704188. ISSN 0022-2488.
Kadison, Richard V. (1 February 1965). "Transformations of states in operator theory and dynamics". Topology. 3: 177–198. doi:10.1016/0040-9383(65)90075-3. ISSN 0040-9383.