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Tracking down gauge: an ode to the constrained Hamiltonian formalism

Earman, John (2003) Tracking down gauge: an ode to the constrained Hamiltonian formalism. In: Symmetries in Physics: Philosophical Reflections. Cambridge University Press, Cambridge, 140 - 162. ISBN 9780521821377

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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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Details

Item Type: Book Section
Status: Published
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Earman, Johnjearman@pitt.eduJEARMAN
Centers: University Centers > Center for Philosophy of Science
Date: 8 December 2003
Date Type: Publication
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Publisher: Cambridge University Press
Place of Publication: Cambridge
Page Range: 140 - 162
DOI or Unique Handle: 10.1017/cbo9780511535369.009
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > History and Philosophy of Science
Refereed: Yes
ISBN: 9780521821377
Title of Book: Symmetries in Physics: Philosophical Reflections
Editors:
EditorsEmailPitt UsernameORCID
Brading, KatherineUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Castellani, ElenaUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Official URL: http://dx.doi.org/10.1017/CBO9780511535369.009
Additional Information: Book DOI: http://dx.doi.org/10.1017/CBO9780511535369
Date Deposited: 24 Jul 2012 18:56
Last Modified: 25 Aug 2017 05:07
URI: http://d-scholarship.pitt.edu/id/eprint/13116

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