Tracking down gauge: An ode to the constrained Hamiltonian formalism

In Katherine Brading & Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press 140--62 (2003)
Abstract
Like moths attracted to a bright light, philosophers are drawn to glitz. So in discussing the notions of ‘gauge’, ‘gauge freedom’, and ‘gauge theories’, they have tended to focus on examples such as Yang–Mills theories and on the mathematical apparatus of fibre bundles. But while Yang–Mills theories are crucial to modern elementary particle physics, they are only a special case of a much broader class of gauge theories. And while the fibre bundle apparatus turned out, in retrospect, to be the right formalism to illuminate the structure of Yang–Mills theories, the strength of this apparatus is also its weakness: the fibre bundle formalism is very flexible and general, and, as such, fibre bundles can be seen lurking under, over, and around every bush. What is needed is an explanation of what the relevant bundle structure is and how it arises, especially for theories that are not initially formulated in fibre bundle language. Here I will describe an approach that grows out of the conviction that, at least for theories that can be written in Lagrangian/Hamiltonian form, gauge freedom arises precisely when there are Lagrangian/Hamiltonian constraints of an appropriate character. This conviction is shared, if only tacitly, by that segment of the physics community that works on constrained Hamiltonian systems.
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Ward Struyve (2011). Gauge Invariant Accounts of the Higgs Mechanism. Studies in History and Philosophy of Science Part B 42 (4):226-236.
John Earman (2006). The “Past Hypothesis”: Not Even False. Studies in History and Philosophy of Science Part B 37 (3):399-430.
Holger Lyre (2004). Holism and Structuralism in (1) Gauge Theory. Studies in History and Philosophy of Science Part B 35 (4):643-670.
Karim P. Y. Thébault (2012). Three Denials of Time in the Interpretation of Canonical Gravity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43 (4):277-294.
Alexandre Guay (2008). A Partial Elucidation of the Gauge Principle. Studies in History and Philosophy of Science Part B 39 (2):346-363.

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