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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Vydáno v:	Studies in History and Philosophy of Modern Physics Ročník 59; s. 44 - 54
Hlavní autoři:	Teh, Nicholas J., Tsementzis, Dimitris
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Ltd 01.08.2017
Témata:	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
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Popis
Shrnutí:	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