Title:
The Relationship between Lagrangian and Hamiltonian Mechanics: The Irregular Case
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 talk, I discuss whether one can extend Barrett’s results to show that Lagrangian and Hamiltonian formulations of gauge theories are equivalent. I show that there is a precise sense in which one can, but that it hinges on philosophical issues concerning the interpretation of symmetries, the criteria for theory equivalence, and the status of excess structure.