  We investigate the infinite volume limit of quantized photon fields in
multimode coherent states. We show that for states containing a continuum of
coherent modes, it is mathematically and physically natural to consider their
phases to be random and identically distributed. The infinite volume states
give rise to Hilbert space representations of the canonical commutation
relations which we construct concretely. In the case of random phases, the
representations are random as well and can be expressed with the help of It\^o
stochastic integrals.
  We analyze the dynamics of the infinite state alone and the open system
dynamics of small systems coupled to it. We show that under the free field
dynamics, initial phase distributions are driven to the uniform distribution.
We demonstrate that coherences in small quantum systems, interacting with the
infinite coherent state, exhibit Gaussian time decay. The decoherence is
qualitatively faster than the one caused by infinite thermal states, which is
known to be exponentially rapid only. This emphasizes the classical character
of coherent states.
