Superselected ghost theory: perturbation theory

Abstract

A superselection rule based on an exact ghost parity can endow a ghost QFT with a probability interpretation. However, this ghost parity is not respected at finite order in the standard perturbative expansion. A ghost-parity-preserving perturbation theory (Z$_2$PT) is obtained through a similarity transformation of the Hamiltonian, $h=g H g^{-1}=h_0+h_1+h_2+...$. The resulting expansion is reminiscent of old-fashioned perturbation theory (OFPT) with some significant differences. The superselection rule selects the principal-value prescription for cross-sector energy denominators, with the prescription determined by the type of transition rather than the particle species. At third order, products of $h_1$ and $h_2$ combine with $h_3$ to reproduce OFPT away from vanishing denominators. At fourth order, when $h_1=0$, we show that $h_2^2$ and $h_4$ satisfy the analogous relation. Contact terms from vanishing denominators distinguish Z$_2$PT from OFPT but do not alter the local primitive UV divergences through these orders.