群平均的婴宇宙场论
Group-averaged baby universe field theory
- University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文从群平均振幅构建婴宇宙场论，阐明其场对易性与线性场方程，并推广至一般拓扑，在特定模型中给出全拓扑的精确福克空间表示。
AI中文摘要：
对时空拓扑的引力求和暗示了一种婴宇宙场论，其量子是完整的宇宙。我们从群平均振幅出发发展这种描述，这些振幅施加引力约束并在单宇宙理论中定义物理内积。为了突出与普通量子场论的对比，我们从一维世界线上的引力开始，这可以通过约化高维柱面得到。对于多个非相互作用的世界线配对边界分量，婴宇宙希尔伯特空间是物理单宇宙希尔伯特空间上的对称福克空间，宇宙场在跨越后者的在壳模式上展开。每个模式乘以产生和湮灭算符之和，因此模式系数对易。模式展开因此明确展示了场的对易性及其惠勒-德威特线性场方程。对角化系数恢复为对标记超选择（α-）扇区的在壳场构型的高斯路径积分的统计描述。我们向更一般的拓扑迈出探索性步骤。盘状拓扑相干移动无边界态，开启哈特尔-霍金波函数作为一点函数。即使由相互作用的费曼图表示非平凡拓扑，我们论证每个边界附近的群平均仍强制相同的线性场方程，而相互作用则通过α-扇区上的非高斯测度进入。在拓扑马罗夫-马克斯菲尔德模型中，我们将盘-柱截断提升为包含所有拓扑的完整理论的精确福克空间表示。我们还通过插入相互作用将截断和精确内积联系起来，其微扰展开产生由裤子对生成的时间演化之和，这让人联想到群平均。
英文摘要：
Gravitational sums over spacetime topology suggest a baby-universe field theory whose quanta are entire universes. We develop such a description from group-averaged amplitudes that impose gravitational constraints and define physical inner products in the single-universe theory. To sharpen the contrast with ordinary QFT, we start with gravity on one-dimensional worldlines, which can arise from reducing higher-dimensional cylinders. For multiple noninteracting worldlines that pair boundary components, the baby-universe Hilbert space is the symmetric Fock space over the physical one-universe Hilbert space, and the universe field expands in the on-shell modes spanning the latter. Each mode multiplies the sum of creation and annihilation operators, so the mode coefficients commute. The mode expansion thus makes explicit the field's commutativity and its Wheeler-DeWitt linear field equation. Diagonalizing the coefficients recovers a statistical description by a Gaussian path integral over on-shell field configurations labelling superselection ($α$-)sectors. We take exploratory steps toward more general topologies. Disk-like topologies coherently shift the no-boundary state, turning on the Hartle-Hawking wavefunction as a one-point function. Even with nontrivial topologies represented by interacting Feynman diagrams, we argue that group averaging near each boundary still enforces the same linear field equation, while interactions instead enter through a non-Gaussian measure over $α$-sectors. In the topological Marolf-Maxfield model, we promote a disk-and-cylinder truncation to an exact Fock-space representation of the full theory incorporating all topologies. We also relate the truncated and exact inner products by an insertion of interactions, whose perturbative expansion produces a sum over time evolutions generated by pairs of pants, evoking an analogy to group averaging.
