Marian J. R. Gilton (University of California, Irvine)
The property of charge is conceptually central to the various gauge theories of fundamental physics. This project develops a geometrical interpretation of charge by comparing and contrasting electric charge and color charge. Color charge is usually introduced as a property in some sense ‘like’ electric charge, playing the same role in the theory of chromodynamics that electric charge plays in the theory of electrodynamics. Knowing only this much about color charge, one might mistakenly expect that color charge will have all the same metaphysical features as electric charge. However, a closer look at these theories shows that the analogy between the two properties does not license such thorough metaphysical similarities. Since these two theories are different in certain crucial respects, we should not expect that the nature of the property that plays the role of charge in each theory is exactly the same.
The main claim of this project is that the charge property at work in gauge theories is best exemplified by color charge and not by electric charge. There are complex features of color charge which are shared by electric charge in principle, but in a degenerate way. In this sense, it is electric charge that is like color charge, and not the other way around. This claim is substantiated on three accounts. First, we consider charge insofar as it is a property attributed to fundamental particles using the mathematics of irreducible representations of Lie groups. Second, this project considers charge as a conserved quantity given by Noether’s theorem as it relates to the metaphysical significance of the Lie algebra. Third, we consider the role of charge in the force laws of gauge theory, using the interpretation of color charge in the Wong force law for chromodynamics to shed light on the standard interpretation of the Lorentz force law for electrodynamics.
