Year: 2025
Type: article
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 characterization of their structure, the two theories are categorically equivalent. However, Barrett only shows equivalence between “hyperregular” models of Lagrangian and Hamiltonian mechanics. While hyperregularity characterizes a large class of theories, it does not characterize 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, and the definition and interpretation of gauge transformations.
Source: Philosophy of Physics
DOI: 10.31389/pop.197
Author: Clara Bradley
Institution: University College London
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413081302