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Charge in Classical Gauge Theories

  • Author(s): Gilton, Marian Judith Rogers
  • Advisor(s): Weatherall, James O
  • et al.
Abstract

This dissertation concerns the philosophical interpretation of charge in contemporary particle physics.

The two most prominent examples of charge are electric charge and color charge. While these two charges are usually described as analogous, it is argued here that they have a number of significant physical and metaphysical differences.

Drawing upon the various group representations used in particle physics as an interpretive basis, it is shown that electric charge in fact has the same mathematical group structure as color charge has, but in a degenerate way. This provides a way of recovering a reversed analogy between color charge and electric charge: it is electric charge that is like color charge, and not vice versa. This reversed analogy is defended in the fifth and final chapter of the dissertation.

This first chapter of the dissertation presents the motivation and scope of the project. The second chapter presents the mathematical framework necessary for drawing these distinctions. This framework includes the formulation of gauge theories on principal fiber bundles and their associated vector bundles, as well as foundational results in the theory of Lie group representations. The third chapter concerns the conservation of charge as a result of Noether's theorem. The Noether charge in non-Abelian gauge theories is interpreted as a union of the opposite properties of color and anti-color. In the fourth chapter, the metaphysical status of these charge properties is brought to the fore. It is often thought that fundamental properties from physics have a privileged status within a scientifically informed ontology of the word. But here, too, the differences between electric charge and color charge have significant ramifications for our understanding of these fundamental properties. While color charge is shown to have a complex three-fold structure, the analogues of these three level collapse in a single level in the case of electric charge. Consequently, the most specific descriptions of color charge lack certain metaphysical virtues had by the most specific descriptions of electric charge.

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