AI 中文总结
研究弯曲时空中量子场论的幺正性，通过幺正压缩算符表述博戈留波夫变换，证明S矩阵的幺正性，得出博戈留波夫内真空由类BCS态描述，还重构了有效哈密顿量等，计算了纠缠熵并推导面积定律。
AI 中文摘要
我们为一般时空中的量子场论提供了幺正性证明。论证通过一个幺正压缩算符来表述博戈留波夫变换，它关联初始和最终希尔伯特空间。弯曲时空中的S矩阵是压缩算符与外希尔伯特空间（通常是闵可夫斯基空间）中S矩阵的乘积，二者皆幺正，其积也幺正。博戈留波夫内真空由类BCS态描述，费米子情形是精确BCS态，只是电子和正电子取代相反自旋电子；玻色子情形是玻色 - 爱因斯坦凝聚超流基态。引力或加速力从真空中创造出对形成库珀对新基态不稳定的多粒子系统。通过反向工程，重构了黑洞（或林德勒）背景下量子场论的有效哈密顿量及质量间隙函数的简单公式，其随温度近似线性增长。随着黑洞质量减小，电子和正电子在越来越高的温度下凝聚成超导态。蒸发各阶段都保持幺正性和粒子解释，霍金态正是BCS态。最后计算了纠缠熵并推导了面积定律。
英文摘要
We provide a proof of unitarity for quantum field theory in a general spacetime. Our argument expresses the Bogoliubov transformations in terms of a unitary squeezing operator relating the initial and final Hilbert spaces. The $S$-matrix in curved spacetime is thus the product of the squeezing operator and the $S$-matrix in the out-Hilbert space (typically Minkowski). Since both factors are unitary, their product is unitary. It follows that the Bogoliubov in-vacuum is described by a BCS-like state (Bardeen--Cooper--Schrieffer): (i) for fermions, it is exactly the BCS state, but with electrons and positrons in place of electrons with opposite spin; (ii) for bosons, it is the Bose--Einstein condensate (BEC) superfluid ground state. Thus, gravity, or an accelerating force, creates from the vacuum a many-particle system unstable towards forming a new ground state of Cooper pairs. Technically, gravity converts the vacuum into an electron-positron condensate, with respect to which quantum field theory evolves unitarily. By reverse engineering, we reconstruct the effective Hamiltonian of QFT in a black hole (or Rindler) background, together with a simple formula for the mass gap function, which grows approximately linearly with the temperature. Hence, electrons and positrons condense into a superconducting state at increasingly higher temperatures as the black hole mass decreases. Unitarity and the particle interpretation are preserved at every stage of evaporation. The Hawking state is exactly a BCS state. Finally, we compute the entanglement entropy and derive the area law.
Comments41 pages, 22 figures. arXiv admin note: text overlap with arXiv:quant-ph/0603269 by other authors
