AI 中文总结
本文采用泛函方法研究弯曲时空中的四费米子凝聚，计算标量道NJL平均场对能量动量张量的单圈局域贡献，推导对应能量密度和压强，验证常数凝聚极限与平直空间结果一致，并说明BCS配对相关内容。
AI 中文摘要
四费米子相互作用出现在粒子物理、多体系统以及含费米子的引力理论的有效描述中。尽管同一局域算符可能出现在微扰散射、真空Nambu-Jona-Lasinio（NJL）不稳定性或有限密度Bardeen-Cooper-Schrieffer（BCS）配对中，但这些 regime 由其相互作用道、二次核和量子态区分。我们对这些区分给出教学性的泛函说明，并计算标量道NJL平均场在弯曲时空中对能量动量张量的单圈局域贡献。我们首先展示in-out泛函中的态数据，并构造in-in期望值所需的闭合时间路径泛函。对于NJL鞍点，Hubbard-Stratonovich场会改变费米子质量，且偶宇称狄拉克行列式产生局域体积、曲率和曲率平方算符。我们在专门到空间平坦FLRW背景前找到协变量子有效作用量，并推导对应的能量密度和压强。常数凝聚极限与直接平直空间平均场计算一致。我们还解释有限密度BCS配对所需的额外态和道数据，并评述弯曲时空中的重整化条件。
英文摘要
Four-fermion interactions appear in effective descriptions of particle physics, many-body systems, and gravitational theories with fermions. Although the same local operator may enter perturbative scattering, a vacuum Nambu-Jona-Lasinio (NJL) instability, or finite-density Bardeen-Cooper-Schrieffer (BCS) pairing, these regimes are distinguished by their interaction channels, quadratic kernels, and quantum states. We give a pedagogical functional account of these distinctions and compute the local one-loop contribution of a scalar-channel NJL mean field to the energy-momentum tensor in curved spacetime. We first display the state data in the in-out functional and construct the closed-time-path functional required for an in-in expectation value. For the NJL saddle, a Hubbard-Stratonovich field shifts the fermion mass, and the parity-even Dirac determinant generates local volume, curvature, and curvature-squared operators. We find the covariant quantum effective action before specializing to a spatially flat FLRW background and derive the corresponding energy density and pressure. The constant-condensate limit agrees with the direct flat-space mean-field calculation. We also explain which additional state and channel data are required for finite-density BCS pairing and comment on renormalization conditions in curved spacetimes.
Comments39 pages, 2 figures
