超选鬼场理论：实谱
Superselected ghost theory: real spectrum
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中文总结 AI 辅助
本文针对带鬼场量子场论的负范数态概率诠释问题，以可重整化量子引力为背景，利用精确鬼宇称$\text{Z}_2$对称性$\text{Q}$作为超选荷，构造出无复极点、概率诠释明确的实谱理论，得到逐阶保留自由鬼宇称的厄米微扰论。
中文摘要 AI 辅助
带有鬼场的量子场论可以是幺正且微扰稳定的，但它们守恒不定内积的负范数态会阻碍概率诠释。这个问题对可重整化量子引力尤为重要。本文聚焦实谱 regime，其中相互作用哈密顿量具有精确的$\boldsymbol{\text{Z}_2}$对称性$\boldsymbol{Q}$，称为精确鬼宇称。它在每个能量本征态上的本征值等于范数的符号，且在零耦合时退化为自由鬼宇称。将$\boldsymbol{Q}$作为超选荷施加，定义了一种新理论，其中物理态具有确定的鬼宇称，可观测量与$\boldsymbol{Q}$对易。此时原生玻恩定则给出非负概率，而光学定理获得直接的概率诠释。传播子分解为具有固定符号谱函数的$\boldsymbol{Q}$-区谱表示，且在物理叶上无复极点。最后，通过相似变换得到一种厄米微扰论，其逐阶保留自由鬼宇称，使精确超选结构在微扰下显现。
英文摘要
Quantum field theories with ghosts can be unitary and perturbatively stable, yet the negative-norm states of their conserved indefinite inner product obstruct a probabilistic interpretation. This problem is especially relevant to renormalizable quantum gravity. The focus of this paper is the real-spectrum regime, in which the interacting Hamiltonian has an exact $\mathbb{Z}_2$ symmetry $Q$, called exact ghost parity. Its eigenvalue on each energy eigenstate equals the sign of the norm, and it reduces to free ghost parity at zero coupling. Imposing $Q$ as a superselection charge defines a new theory in which the physical states have definite ghost parity and the observables commute with $Q$. The native Born rule then yields non-negative probabilities, while the optical theorem acquires a direct probabilistic interpretation. The propagator decomposes into $Q$-sector spectral representations with fixed-sign spectral functions and no complex poles on the physical sheet. Finally, a similarity transformation yields a Hermitian perturbation theory that preserves free ghost parity order by order, making the exact superselection structure perturbatively manifest.
