Minimum-uncertainty states of systems with many degrees of freedom

The minimum-uncertainty states for systems with many degrees of freedom are investigated. The limiting situation, relevant to the electromagnetic field, is discussed and it is pointed out that the states that minimize Δp Δq do not tend to the coherent states. These latter, including the vacuum state, are minimum-uncertainty states for the transverse electric and magnetic fields. In an appendix a direct method to obtain the wave functional for the vacuum is presented.