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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Veröffentlicht in:Studies in History and Philosophy of Modern Physics Jg. 59; S. 44 - 54
Hauptverfasser: Teh, Nicholas J., Tsementzis, Dimitris
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.08.2017
Schlagworte:
Classical mechanics and symplectic geometry
Common definitional extension
Definability
Legendre transformation
Physical dualities in quantum field theory and string theory
Theoretical equivalence
Common definitional extension
Theoretical equivalence
Definability
Physical dualities in quantum field theory and string theory
Classical mechanics and symplectic geometry
Legendre transformation
ISSN:1355-2198, 1879-2502
Online-Zugang:Volltext
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Zusammenfassung: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’.
ISSN:1355-2198
1879-2502
DOI:10.1016/j.shpsb.2016.02.002