发表机构
Universidade Federal da Paraíba（帕拉伊巴联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构建弯曲时空中的非局域自旋-1/2场论，推导非局域狄拉克方程，并在德西特时空构造非局域Bunch--Davies模式，证明其解析结构保持且可平滑回归局域理论。
AI 中文摘要
我们在弯曲时空中构建了一个自旋-1/2的非局域场论，其中形状因子是协变狄拉克算符的非多项式整函数。我们推导了相应的非局域狄拉克方程，并分析了其与引力及U(1)规范场的耦合。作为应用，我们在德西特时空的开图中研究该理论，并构造了相关的非局域Bunch--Davies模式。非局域动力学可以逐分支地映射到具有有效质量M_n的局域狄拉克方程上。对于此处考虑的指数形状因子，有效质量用Lambert-W函数的分支表示。我们证明了Bunch--Davies构造的欧几里得解析结构得以保持。在物理的正留数分支上，Bogoliubov系数、压缩参数、占据数和纠缠熵获得了显式的非局域修正，而物理费米子超曲率模式的缺失得以保持。在Λ→∞极限下，局域理论平滑地恢复。
英文摘要
We formulate a nonlocal spin-$1/2$ field theory in curved spacetime in which the form factor is a nonpolynomial entire function of the covariant Dirac operator. We derive the corresponding nonlocal Dirac equation and analyze its coupling to gravity and to a $\rm U(1)$ gauge field. As an application, we study the theory in the open chart of de Sitter spacetime and construct the associated nonlocal Bunch--Davies modes. The nonlocal dynamics can be mapped, branch by branch, onto the local Dirac equation with an effective mass $M_n$. For the exponential form factors considered here, the effective masses are expressed in terms of branches of the Lambert-$W$ function. We show that the Euclidean analyticity structure of the Bunch--Davies construction is preserved. On the physical positive-residue branch, the Bogoliubov coefficients, squeezing parameter, occupation number, and entanglement entropy acquire explicit nonlocal corrections, while the absence of physical fermionic supercurvature modes is preserved. The local theory is smoothly recovered in the limit $Λ\to\infty$.
Comments21 pages, 1 figure
