Causally neutral quantum physics

In fundamental theories that accounts for quantum gravitational effects, the spacetime causal structure is expected to be quantum uncertain. Previous studies of quantum causal structure focused on finite-dimensional systems. Here we present an algebraic framework that incorporates both finite- and infinite-dimensional systems including quantum fields. Thanks to the absence of a definite spacetime causal structure, Lagrangian quantum field theories can be studied on a quantum superposition of spacetimes with a point identification structure.