%0 Generic %1 betzios2020black %A Betzios, Panos %A Gaddam, Nava %A Papadoulaki, Olga %D 2020 %K physics %T Black holes, quantum chaos, and the Riemann hypothesis %U http://arxiv.org/abs/2004.09523 %X 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 dynamics of the scattering matrix on a Schwarzschild black hole background, given the rich chaotic spectrum upon discretisation. It also explains why the spectrum appears to be erratic despite the unitarity of the scattering matrix.

@misc{betzios2020black, abstract = {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 dynamics of the scattering matrix on a Schwarzschild black hole background, given the rich chaotic spectrum upon discretisation. It also explains why the spectrum appears to be erratic despite the unitarity of the scattering matrix.}, added-at = {2020-05-20T09:10:21.000+0200}, author = {Betzios, Panos and Gaddam, Nava and Papadoulaki, Olga}, biburl = {https://www.bibsonomy.org/bibtex/2a7311e4a85614d776fc1ba342bb83634/simonechiarello}, description = {Black holes, quantum chaos, and the Riemann hypothesis}, interhash = {c75331266806f26a189ac15b8482c6e2}, intrahash = {a7311e4a85614d776fc1ba342bb83634}, keywords = {physics}, note = {cite arxiv:2004.09523Comment: 11 pages, improved presentation, results unchanged}, timestamp = {2020-05-20T09:10:21.000+0200}, title = {Black holes, quantum chaos, and the Riemann hypothesis}, url = {http://arxiv.org/abs/2004.09523}, year = 2020 }