Extend the source-field framework to many-body and quantum-field systems

Determine whether the Schrödinger source field for an N-particle de Broglie-Bohm system should be defined on the 3N-dimensional configuration space or on spacetime, and develop the corresponding extension to systems with infinitely many degrees of freedom and to quantum field theory.

Background

The paper formulates J on the configuration space of a single-particle system. Extending the construction to many-body systems raises a choice between preserving the nonlocal configuration-space formulation and pursuing a spacetime-local reformulation. Quantum-field-theoretic extension additionally requires clarifying the relation between J and conventional field sources such as currents and energy-momentum tensors.

References

The generalization to $N$-particle systems raises the question of whether $J$ should be defined on the $3N$-dimensional configuration space---preserving the manifest nonlocality characteristic of dBB dynamics---or on spacetime, which would require a more radical reformulation of the pilot-wave framework in terms of local beables.

— de Broglie-Bohm Dynamics with Schrödinger Source Fields: A Framework for Subquantum Theory  (2608.13894 - Mikki, 14 Aug 2026) in Section 'Future Directions', subsection 'Extension to many-body systems and quantum fields'