Physical distinction among alternative vacuum states in flat spacetime geometries

Even in flat spacetime, the states of a quantized field can be described via a variety of inequivalent Fock-space representations, associated with different congruences of inertial or noninertial observers. But it appears possible to distinguish among the possibilities on physical grounds: Field positive- and negative-frequency eigenfunctions might be required to be well defined and regular throughout the spacetime, so that the states can be attained by evolution from regular data in the remote past. This criterion distinguishes the familiar Minkowski-coordinate construction from that corresponding to the diverging congruence of observers whose world lines trace out a degenerate-Kasner subspace of Minkowski spacetime, for example. It also draws a physical distinction between the Minkowski-coordinate Fock-space states and those associated with a congruence of uniformly accelerated observers (Rindler observers); the latter states cannot be represented as any combinations of the former. This analysis of alternative descriptions of a quantized field may extend to more general classes of observers, and to more general spacetime geometries as well.