Identity in Gauge Theories

I argue that contemporary theories of physics are best understood as involving a more refined identity relation than the one found in first order logic. I use this identity relation to provide novel interpretations of Yang–Mills theory and General Relativity, two of the most successful physical theories. I show that my interpretation is superior to those currently on the market because it solves problems left open by extant interpretations and provides a better explanation of the distinctive features of these theories. My interpretation also fills gaps in justification found in the physics literature