Abstract:
Gravitational sums over spacetime topology suggest a baby-universe field theory whose quanta are entire universes. We further develop such a description starting from group-averaged amplitudes that impose gravitational constraints and define physical inner products in the single-universe theory. To sharpen the contrast with ordinary QFT, we start with gravity on one-dimensional worldlines, which can arise from reducing higher-dimensional cylinders. For multiple noninteracting worldlines that pair boundary components, the baby-universe Hilbert space is the symmetric Fock space over the physical one-universe Hilbert space. The universe field admits an expansion in on-shell modes that span the latter and satisfy the Wheeler-DeWitt constraint as a field equation of motion. Unlike QFT, we find that each mode multiplies the sum of universe creation and annihilation operators, without reference to any positive-/negative-frequency split. The overall coefficients of different modes mutually commute and the universe field consequently commutes at any two points in the worldline target space. Diagonalizing the coefficients recovers a statistical description by a Gaussian path integral over on-shell field configurations labelling superselection (alpha-)sectors. Time permitting, we will end with some exploratory comments on extending this framework to more general spacetime topologies allowing universes to cap off, split, and join.