Bradley, Clara (2024) The Relationship Between Lagrangian and Hamiltonian Mechanics: The Irregular Case. [Preprint]

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Abstract

Lagrangian and Hamiltonian mechanics are widely held to be two distinct but equivalent ways of formulating classical theories. Barrett (2019) makes this intuition precise by showing that under a certain characterisation of their structure, the two theories are categorically equivalent. However, Barrett only shows equivalence between “hyperregular” models of Lagrangian and Hamiltonian mechanics. While hyperregularity characterises a large class of theories, it does not characterise the class of gauge theories. In this paper, I consider whether one can extend Barrett’s results to show that Lagrangian and Hamiltonian formulations of gauge theories are equivalent. I argue that there is a precise sense in which one can, and I illustrate that exploring this question highlights several interesting questions about the way that one can construct models of Hamiltonian mechanics from models of Lagrangian mechanics and vice versa, about the role that constraints play, as well as the definition and interpretation of gauge transformations.

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Item Type:	Preprint
Creators:	Creators Email ORCID Bradley, Clara clarajbradley@gmail.com
Subjects:	Specific Sciences > Physics > Classical Physics General Issues > Structure of Theories Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Clara Bradley
Date Deposited:	28 Aug 2024 03:35
Last Modified:	28 Aug 2024 03:35
Item ID:	23799
Subjects:	Specific Sciences > Physics > Classical Physics General Issues > Structure of Theories Specific Sciences > Physics > Symmetries/Invariances
Date:	27 August 2024
URI:	https://philsci-archive.pitt.edu/id/eprint/23799

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