Time Asymmetric Quantum Mechanics
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2011 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147386 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Time Asymmetric Quantum Mechanics / A.R. Bohm, M. Gadella, P. Kielanowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862620745570451456 |
|---|---|
| author | Bohm, A.R. Gadella, M. Kielanowski, P. |
| author_facet | Bohm, A.R. Gadella, M. Kielanowski, P. |
| citation_txt | Time Asymmetric Quantum Mechanics / A.R. Bohm, M. Gadella, P. Kielanowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t₀≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.
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| first_indexed | 2025-12-07T13:22:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147386 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:22:30Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bohm, A.R. Gadella, M. Kielanowski, P. 2019-02-14T16:55:51Z 2019-02-14T16:55:51Z 2011 Time Asymmetric Quantum Mechanics / A.R. Bohm, M. Gadella, P. Kielanowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q65 https://nasplib.isofts.kiev.ua/handle/123456789/147386 The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t₀≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics. This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
 We wish to acknowledge partial financial support by the Spanish Ministry of Science and Innovation through Project MTM2009-10751, the Junta de Castilla y Le´on, through Project GR224 and the US NSF Award no OISE-0421936. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Time Asymmetric Quantum Mechanics Article published earlier |
| spellingShingle | Time Asymmetric Quantum Mechanics Bohm, A.R. Gadella, M. Kielanowski, P. |
| title | Time Asymmetric Quantum Mechanics |
| title_full | Time Asymmetric Quantum Mechanics |
| title_fullStr | Time Asymmetric Quantum Mechanics |
| title_full_unstemmed | Time Asymmetric Quantum Mechanics |
| title_short | Time Asymmetric Quantum Mechanics |
| title_sort | time asymmetric quantum mechanics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147386 |
| work_keys_str_mv | AT bohmar timeasymmetricquantummechanics AT gadellam timeasymmetricquantummechanics AT kielanowskip timeasymmetricquantummechanics |