Superselected ghost theory: entangled pairs
The superselection-rule approach to ghost theories is extended to theories with a nonreal spectrum containing a complex-conjugate pair of poles on the physical sheet. The two excitations are labeled by their respective complex masses, $M$ and $M^*$, and the superselection sectors are labeled by $n$, the difference between the numbers of $M$ and $M^*$ excitations. The corresponding generalized ghost parity $Q$ assigns a phase $e^{in\alpha}$ to each sector. Under $Q$ superselection, nonvanishing norms occur only in the $n=0$ sector, and the physical state condition $Q^{2}|s\rangle=|s\rangle$ projects onto this sector. For a $MM^*$ pair carrying real total energy and momentum, we define a swap operation $R$. The $R$-eigenstates are entangled pairs, and an $R$ superselection rule ensures positive probabilities. We discuss how the optical theorem describes physical cuts through these entangled pairs.