Theoretical equivalence in classical mechanics and its relationship to duality
As a prolegomenon to understanding the sense in which dualities are theoretical equivalences, we investigate the intuitive ‘equivalence’ of hyper-regular Lagrangian and Hamiltonian classical mechanics. We show that the symplectification of these theories (via Tulczyjew׳s Triple) provides a sense in...
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| Vydané v: | Studies in History and Philosophy of Modern Physics Ročník 59; s. 44 - 54 |
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01.08.2017
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| Abstract | As a prolegomenon to understanding the sense in which dualities are theoretical equivalences, we investigate the intuitive ‘equivalence’ of hyper-regular Lagrangian and Hamiltonian classical mechanics. We show that the symplectification of these theories (via Tulczyjew׳s Triple) provides a sense in which they are (1) isomorphic, and (2) mutually and canonically definable through an analog of ‘common definitional extension’. |
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| AbstractList | As a prolegomenon to understanding the sense in which dualities are theoretical equivalences, we investigate the intuitive ‘equivalence’ of hyper-regular Lagrangian and Hamiltonian classical mechanics. We show that the symplectification of these theories (via Tulczyjew׳s Triple) provides a sense in which they are (1) isomorphic, and (2) mutually and canonically definable through an analog of ‘common definitional extension’. |
| Author | Tsementzis, Dimitris Teh, Nicholas J. |
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| Cites_doi | 10.1007/s10992-015-9382-6 10.5840/jphil2009106213 10.1090/S0273-0979-1981-14911-9 10.1086/664745 10.1017/S0305004111000624 10.1086/392812 10.1112/jlms/s2-33.1.1 10.1002/malq.200410051 |
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| Keywords | Common definitional extension Theoretical equivalence Definability Physical dualities in quantum field theory and string theory Classical mechanics and symplectic geometry Legendre transformation |
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| SubjectTerms | Classical mechanics and symplectic geometry Common definitional extension Definability Legendre transformation Physical dualities in quantum field theory and string theory Theoretical equivalence |
| Title | Theoretical equivalence in classical mechanics and its relationship to duality |
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