Computing the Lagrangians of the Standard Model II. The Ghost Term

Abstract

We follow up an earlier attempt to compute the Yang–Mills Lagrangian density from first principles. In that work, the Lagrangian density emerged replete with a Feynman–’t Hooft gauge fixing term. In this note we find that similar methods may be applied to produce the concomitant ghost term. Our methods are elementary and entirely and straightforwardly algebraic. Insofar as one of our first principles in the earlier computation was the Schwinger Action Principle, which is a differential version of the Feynman path integral, our computation here may be viewed as a differential version of the Faddeev–Popov functional integral approach to generating the ghost Lagrangian. As such, it avoids all measure theoretic difficulties and ambiguities, though at the price of generality.