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  • Cited by 11
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    Earman, John 2003. The cosmological constant, the fate of the universe, unimodular gravity, and all that. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Vol. 34, Issue. 4, p. 559.

    Brown*, Harvey R. and Holland†, Peter 2004. Dynamical versus variational symmetries: understanding Noether's first theorem. Molecular Physics, Vol. 102, Issue. 11-12, p. 1133.

    Earman, John 2004. Laws, Symmetry, and Symmetry Breaking: Invariance, Conservation Principles, and Objectivity. Philosophy of Science, Vol. 71, Issue. 5, p. 1227.

    Earman, J. 2006. Two Challenges to the Requirement of Substantive General Covariance. Synthese, Vol. 148, Issue. 2, p. 443.

    Rickles, Dean Smeenk, Chris Lyre, Holger and Healey, Richard 2009. Gauge Pressure. Metascience, Vol. 18, Issue. 1, p. 5.

    Silberstein, Michael Stuckey, W. M. and McDevitt, Timothy 2013. Being, Becoming and the Undivided Universe: A Dialogue Between Relational Blockworld and the Implicate Order Concerning the Unification of Relativity and Quantum Theory. Foundations of Physics, Vol. 43, Issue. 4, p. 502.

    Huggett, Nick Vistarini, Tiziana and Wüthrich, Christian 2013. A Companion to the Philosophy of Time. p. 242.

    Chen, Chiang-Mei Nester, James M. and Tung, Roh-Suan 2015. Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach. International Journal of Modern Physics D, Vol. 24, Issue. 11, p. 1530026.

    Gryb, Sean and Thébault, Karim P. Y. 2016. Time Remains. The British Journal for the Philosophy of Science, Vol. 67, Issue. 3, p. 663.

    Nester, James M. and Chen, Chiang-Mei 2016. Gravity: A gauge theory perspective. International Journal of Modern Physics D, Vol. 25, Issue. 13, p. 1645002.

    Wüthrich, Christian 2017. Towards a Theory of Spacetime Theories. Vol. 13, Issue. , p. 297.

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  • Print publication year: 2003
  • Online publication date: October 2009

8 - Tracking down gauge: an ode to the constrained Hamiltonian formalism

Summary

Introduction

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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Symmetries in Physics
  • Online ISBN: 9780511535369
  • Book DOI: https://doi.org/10.1017/CBO9780511535369
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