Bosonic field equations from an exact uncertainty principle

Abstract

A Hamiltonian formalism is used to describe ensembles of fields in terms of two canonically conjugate functionals (one being the field probability density). The postulate that a classical ensemble is subject to nonclassical fluctuations of the field momentum density, of a strength determined solely by the field uncertainty, is shown to lead to a unique modification of the ensemble Hamiltonian. The modified equations of motion are equivalent to the quantum equations for a bosonic field, and thus this exact uncertainty principle provides a new approach to deriving and interpreting the properties of quantum ensembles. The examples of electromagnetic and gravitational fields are discussed. In the latter case the exact uncertainty approach specifies a unique operator ordering for the Wheeler-DeWitt and Ashtekar-Wheeler-DeWitt equations.

24 pages, extended version of part (B) of hep-th/0206235, to appear in J. Phys. A

References in corpus (3)

• Schrodinger equation from an exact uncertainty principle
• Operator ordering and consistency of the wavefunction of the Universe
• Quantum mechanics from a Heisenberg-type equality

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