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Baby Universes and Worldline Field Theories
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The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra of quantum fields, while the former has been argued to define an abelian algebra of superselected observables associated with partition-function-like quantities at an asymptotic boundary. We resolve this apparent tension by pointing out a variety of discrete choices that must be made in constructing a Hilbert space from such path integrals, and arguing that the natural choices for quantum gravity differ from those used to construct QFTs. We focus on one-dimensional models of quantum gravity in order to make direct comparisons with worldline QFT.
Forward citations
Cited by 2 Pith papers
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The $\alpha$-states of a string worldsheet
The α-states of the Hurwitz worldsheet are symmetric-group characters weighted by the Poissonized Plancherel measure, so string amplitudes are ensemble averages whose weak-coupling limit is Kerov's central limit theorem.
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Observers and Timekeepers: From the Page-Wootters Mechanism to the Gravitational Path Integral
Metric summation produces the problem of time, topology summation produces the one-dimensional Hilbert space, and a timekeeper path integral gives observer-dependent holography.
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