Superselected ghost theory: entangled pairs
Abstract
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 einα to each sector. Under Q superselection, nonvanishing norms occur only in the n=0 sector, and the physical state condition Q2|s⟩=|s⟩ 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.
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BibTeX
@misc{holdom2026superselected,
title = {{Superselected ghost theory: entangled pairs}},
author = {Bob Holdom},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04342},
eprint = {2609.04342},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04342},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Superselected ghost theory: entangled pairs
AU - Bob Holdom
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04342
UR - https://arxiv.org/abs/2609.04342
AB - 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^inα to each sector. Under Q superselection, nonvanishing norms occur only in the n=0 sector, and the physical state condition Q^2|s⟩=|s⟩ 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.
ER -