  We present a unified field theory of wave and particle in quantum mechanics.
This emerges from an investigation of three weaknesses in the de Broglie-Bohm
(deBB) theory: its reliance on the quantum probability formula to justify the
particle law; its insouciance regarding the absence of reciprocal action of the
particle on the guiding wave; and its lack of a unified model to represent its
inseparable components. These problems are resolved within an analytical
framework by requiring that the wave-particle composite exhibits no observable
differences with a quantum system. This scheme is implemented by appealing to
symmetries (global gauge and spacetime translations) and imposing equality of
the corresponding conserved Noether densities (matter, momentum and energy)
with their Schrodinger counterparts. In conjunction with the condition of time
reversal covariance this implies the deBB law for the particle where the
quantum potential mediates the wave-particle interaction (we also show how the
time reversal assumption may be replaced by a statistical condition). The
method clarifies the nature of the mass of the composite, and its
energy-momentum conservation laws. Our principal result is the unification of
the Schrodinger equation and the deBB law in an inhomogeneous equation whose
solution amalgamates the wavefunction and a singular soliton model of the
particle in a unified spacetime field. The wavefunction suffers no reaction
from the particle since it is the homogeneous part of the unified field to
whose source the particle contributes. The theory applies to many-body systems.
We review the objections of de Broglie to the pilot-wave theory and suggest
that our field-theoretic model provides a realization of his hitherto
unfulfilled double-solution programme. A revised set of postulates for the deBB
theory is given in which the unified field is taken as the basic descriptive
element.
