Clara Bradley (UCL): ‘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 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.

Clara Bradley is a Lecturer (Assistant Professor) in the Department of Philosophy at University College London (UCL).

This event will take place in person on LSE’s campus. However, those unable to attend in person will have the option of taking part online.

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