Hawking’s seminal work on black hole radiation highlights a critical issue in our understanding of quantum field theory in curved spacetime (QFTCS), specifically the problem of unitarity loss (where pure states evolve into mixed states). In this paper, we examine a recent proposal for a direct-sum QFTCS, which maintains unitarity through a novel quantization method that employs geometric superselection rules based on discrete spacetime transformations. This approach describes a quantum state in terms of components that evolve within geometric superselection sectors of the complete Hilbert space, adhering to the discrete symmetries of a Schwarzschild black hole. Consequently, it represents a maximally entangled pure state as a direct-sum of two components in the interior and exterior regions of the black hole, thereby preserving the unitarity of Hawking radiation by keeping it in the form of pure states.

霍金在黑洞辐射方面的开创性工作突出了我们理解弯曲时空量子场论 （QFTCS） 的一个关键问题，特别是幺正性损失问题（纯态演变为混合态）。在本文中，我们研究了最近提出的直接和 QFTCS 提案，该方法通过一种新的量化方法保持幺正性，该方法采用基于离散时空变换的几何超选规则。这种方法根据在整个希尔伯特空间的几何超选择扇区内演化的分量来描述量子态，这些分量遵循史瓦西黑洞的离散对称性。因此，它表示一个最大纠缠的纯态，即黑洞内部和外部区域中两个分量的直接和，从而通过保持霍金辐射的纯态形式来保持霍金辐射的幺正性。