Bosonic zero-frequency modes and initial conditions

Zero-frequency modes for massless scalar and vector fields are considered. Although these modes lack a particle interpretation, they may nonetheless be quantized. It is shown how the quantum field theory of such massless fields contains an arbitrary parameter which determines the energy associated with the zero mode. We then show how this parameter may be related to initial conditions in a model theory with a time-dependent mass which vanishes in the future. The energy carried by the zero mode is determined by the original particle content of the quantum state and the details of how the mass varies in time. These considerations are applied to scalar and vector fields in flat spacetime with periodic boundary conditions and in Robertson-Walker universes. The connection between scalar zero modes and global symmetry breaking is discussed, especially the conditions under which broken-symmetry states decay in time due to zero-mode effects.