The Hartle-Hawking state for toroidal quantum cosmologies is expressed in the Langlands decomposition as a sum over zeta zeros whose near-singularity dynamics follow the Hilbert-Pólya Hamiltonian and as a Möbius average of CFT partition functions.
Witten,A note on the canonical formalism for gravity, Adv
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Reviews construction of physical inner products in canonical quantum gravity via group averaging and BRST formalism, illustrated in mini-superspace models and connected to path integrals.
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M\"obius randomness in the Hartle-Hawking state
The Hartle-Hawking state for toroidal quantum cosmologies is expressed in the Langlands decomposition as a sum over zeta zeros whose near-singularity dynamics follow the Hilbert-Pólya Hamiltonian and as a Möbius average of CFT partition functions.
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Gravitational Hilbert spaces: invariant and co-invariant states, inner products, gauge-fixing, and BRST
Reviews construction of physical inner products in canonical quantum gravity via group averaging and BRST formalism, illustrated in mini-superspace models and connected to path integrals.