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...

Full description

Saved in:
Bibliographic Details
Published in:Studies in History and Philosophy of Modern Physics Vol. 59; pp. 44 - 54
Main Authors: Teh, Nicholas J., Tsementzis, Dimitris
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.08.2017
Subjects:
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 Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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