Boundary conditions for the Klein-Gordon field on Lifshitz spacetimes

Boundary conditions have physical consequences. On Lifshitz spacetimes, the Klein-Gordon equation gives rise to an initial-boundary value problem that admits a plethora of physically-sensible boundary conditions. Considering a free, scalar, massive quantum field theory on a four-dimensional Lifshitz spacetime with critical exponent z = 2, I layout how to construct two-point functions for ground and thermal states, of local Hadamard form, satisfying the canonical commutation relations, and compatible with Robin and mode-dependent boundary conditions. Each one relates to an inequivalent dynamics, but they are all equivalently physically-sensible-only an experiment could single one out. The results I present here are part of a joint work with C. Dappiaggi and D. Sina.