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This paper sets up a perturbative treatment of the evolving quantum state ofa gravitational system, in a Schr\"odinger-like picture, working about ageneral background. This connects gauge symmetry, the constraints,gravitational dressing, and evolution. Starting with a general time slicing, wegive a simple derivation of the relation between the constraints, thehamiltonian, and its well-known boundary term. Among different approaches toquantization with constraints, we focus on a "gauge-invariant canonicalquantization," which is developed perturbatively in the gravitational coupling.The leading-order solution of the constraints (including the Wheeler-DeWittequation) for perturbations about the background is given in terms of anexplicit construction of gravitational dressings built using certaingeneralized Green functions; different such dressings corresponding to addingpropagating gravitational waves to a particular solution of the constraints.Dressed operators commute with the constraints, expressing their gaugeinvariance, and have an algebraic structure differing significantly from theundressed operators of the underlying field theory. These operators can act onthe vacuum to create dressed states, and evolution of general such states isthen generated by the boundary hamiltonian, and alternately may becharacterized using other relational observables. This provides a concreteapproach to studying perturbative time evolution, including the leadinggravitational backreaction, of quantum states of black holes with flat or antide Sitter asymptotics, for example on horizon-crossing slices. This descriptionof evolution in turn provides a starting point for investigating possiblyimportant corrections to quantum evolution, that go beyond quantized generalrelativity.

Perturbative quantum evolution of the gravitational state and dressing in general backgrounds