Exact uncertainty properties of bosonic fields

TL;DR

This paper establishes an exact uncertainty relation for bosonic quantum fields, providing a new approach to derive and interpret these fields through a principle linking classical and nonclassical momentum fluctuations.

Contribution

It introduces an exact uncertainty relation for bosonic fields and develops a novel framework for deriving quantum field equations from classical ensembles.

Findings

Derives an exact uncertainty relation for bosonic fields.

Proposes a new approach to quantum field derivation based on uncertainty principles.

Determines a unique operator ordering for the Wheeler-deWitt equation in quantum gravity.

Abstract

(A) The momentum density conjugate to a bosonic quantum field splits naturally into the sum of a classical component and a nonclassical component. It is shown that the field and the nonclassical component of the momentum density satisfy an_exact_ uncertainty relation, i.e., an equality, which underlies the Heisenberg-type uncertainty relation for fields. (B) The above motivates a new approach to deriving and interpreting bosonic quantum fields, based on an exact uncertainty principle. In particular, the postulate that an ensemble of classical fields is subject to nonclassical momentum fluctuations, of a strength determined by the field uncertainty, leads from the classical to the quantum field equations. Examples include scalar, electromagnetic and gravitational fields. For the latter case the exact uncertainty principle specifies a unique (non-Laplacian) operator ordering for the Wheeler-deWitt equation.