论文标题
黑洞，量子混乱和Riemann假设
Black holes, quantum chaos, and the Riemann hypothesis
论文作者
论文摘要
量子重力有望在紫外线中衡量有效理论的所有全局对称性。受到期望的启发，我们探讨了将CPT作为相空间中量子边界条件的后果。我们发现，它提供了与扩张算子相关的量子哈密顿量的连续光谱的自然半经典化和离散化。我们观察到所述频谱与Riemann Zeta和Dirichlet Beta函数的零相对应。遵循浆果和济彩的想法，这可能有助于追求里曼假设。它加强了这一建议，即这种量子哈密顿量捕获了施瓦茨柴尔德黑洞的散射矩阵的近地平线动力学，鉴于离散后具有丰富的混乱谱。它还解释了为什么尽管散射矩阵的单位性，频谱似乎仍然不稳定。
Quantum gravity is expected to gauge all global symmetries of effective theories, in the ultraviolet. Inspired by this expectation, we explore the consequences of gauging CPT as a quantum boundary condition in phase space. We find that it provides for a natural semiclassical regularisation and discretisation of the continuous spectrum of a quantum Hamiltonian related to the Dilation operator. We observe that the said spectrum is in correspondence with the zeros of the Riemann zeta and Dirichlet beta functions. Following ideas of Berry and Keating, this may help the pursuit of the Riemann hypothesis. It strengthens the proposal that this quantum Hamiltonian captures the near horizon dynamics of the scattering matrix of the Schwarzschild black hole, given the rich chaotic spectrum upon discretisation. It also explains why the spectrum appears to be erratic despite the unitarity of the scattering matrix.
