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A Hamiltonian formalism is used to describe ensembles of fields in terms oftwo canonically conjugate functionals (one being the field probabilitydensity). The postulate that a classical ensemble is subject to nonclassicalfluctuations of the field momentum density, of a strength determined solely bythe field uncertainty, is shown to lead to a unique modification of theensemble Hamiltonian. The modified equations of motion are equivalent to thequantum equations for a bosonic field, and thus this exact uncertaintyprinciple provides a new approach to deriving and interpreting the propertiesof quantum ensembles. The examples of electromagnetic and gravitational fieldsare discussed. In the latter case the exact uncertainty approach specifies aunique operator ordering for the Wheeler-DeWitt and Ashtekar-Wheeler-DeWittequations.Comment: 24 pages, extended version of part (B) of hep-th/0206235, to appear  in J. Phys.

Bosonic field equations from an exact uncertainty principle