  We study half-space/Rindler modular Hamiltonians for excited states created
by turning on sources for local operators in the Euclidean path integral in
relativistic quantum field theories. We derive a simple, manifestly Lorentzian
formula for the modular Hamiltonian to all orders in perturbation theory in the
sources. We apply this formula to the case of shape-deformed half spaces in the
vacuum state, and obtain the corresponding modular Hamiltonian to all orders in
the shape deformation in terms of products of half-sided null energy operators,
i.e., stress tensor components integrated along the future and past Rindler
horizons. In the special case where the shape deformation is purely null, our
perturbation series can be resummed, and agrees precisely with the known
formula for vacuum modular Hamiltonians for null cuts of the Rindler horizon.
Finally, we study some universal properties of modular flow (corresponding to
Euclidean path integral states) of local operators inside correlation functions
in conformal field theories. In particular, we show how the flow becomes the
local boost in the limit where the operator being flowed approaches the
entanglement cut.
