AI 中文总结
该研究提出保持鬼宇称的微扰论Z₂PT，通过哈密顿相似变换构建，其接触项与老式微扰论OFPT有别，且不改变局域原始紫外发散。
AI 中文摘要
基于精确鬼宇称的超选规则可赋予鬼场量子场论（ghost QFT）概率诠释，但标准微扰展开的有限阶不满足该鬼宇称。通过对哈密顿量做相似变换$h=gHg^{-1}=h_0+h_1+h_2+\dots$，可得到保持鬼宇称的微扰论（Z₂PT），其展开形式与老式微扰论（OFPT）相似但存在显著差异。该超选规则为跨能区能量分母选取主值方案，方案由跃迁类型而非粒子种类决定。三阶时，$h_1$与$h_2$的乘积结合$h_3$可在非零分母处复现OFPT；四阶时，当$h_1=0$，$h_2^2$与$h_4$满足类似关系。来自零分母的接触项使Z₂PT与OFPT区分，但不改变这些阶的局域原始紫外发散。
英文摘要
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.
Comments19 pages
