I ain’t afraid of no ghost

Abstract

This paper criticizes the traditional philosophical account of the quantization of gauge theories and offers an alternative. On the received view, gauge theories resist quantization because they feature distinct mathematical representatives of the same physical state of affairs. This resistance is overcome by a sequence of ad hoc modifications, justified in part by reference to semiclassical electrodynamics. Among other things, these modifications introduce "ghosts": particles with unphysical properties which do not appear in asymptotic states and which are said to be purely a notational convenience. I argue that this sequence of modifications is unjustified and inadequate, making it a poor basis for the interpretation of ghosts. I then argue that gauge theories can be quantized by the same method as any other theory. On this account, ghosts are not purely notation: they are coordinates on the classical configuration space of the theory-specifically, on its gauge structure. This interpretation does not fall prey to the standard philosophical arguments against the significance of ghosts, due to Weingard. Weingard's argumentative strategy, properly applied, in fact tells in favor of ghosts' physical significance.

Effective and Selective Realisms

“…The precise role of redundancy talk in the quantization of electrodynamics is disputed, but generally speaking it is used to solve a problem with applying standard quantization techniques to theories like classical electromagnetism (Redhead, 2003;Healey, 2007;Dougherty, 2021). Heuristically, the path integral is dominated by stationary points of the action, and so to lowest order will reproduce the predictions of a classical field theory with the same action and configuration space.…”