Chern–Simons theory
To canonically quantize Chern–Simons theory one defines a state on each 2-dimensional surface Σ in M. As in any quantum field theory, the states correspond to rays in a Hilbert space. There is no preferred notion of time in a Schwarz-type topological field theory and so one can require that Σ be a Cauchy surface, in fact, a state can be defined on any surface.