Quantum fields from real-time ensemble dynamics

TL;DR

This paper introduces a real-time Schrödinger-picture formulation of quantum field theory where fields evolve as probability ensembles, unifying various QFT concepts and clarifying the distinction between fundamental dynamics and representations.

Contribution

It presents a novel ensemble-based framework for QFT that derives standard formulations and clarifies the origin of correlations and entanglement from underlying ensemble dynamics.

Findings

Reformulates QFT in a real-time ensemble framework

Derives propagators and correlations from ensemble dynamics

Unifies operator, diagrammatic, and path-integral approaches

Abstract

Relativistic quantum field theory (QFT) is commonly formulated in terms of operators, asymptotic states, and covariant amplitudes, a perspective that tends to obscure the real-time origin of field dynamics and correlations. Here we formulate quantum fields in a real-time Schr\"odinger-picture framework, in which fields evolve as probability ensembles on the space of field configurations. Within this formulation, the wavefunctional $\Psi[\phi,t]$ encodes a first-order, causal ensemble dynamics on configuration space. Interactions appear as couplings between configuration-space directions, while propagators arise as derived correlation structures rather than as fundamental postulates. Entanglement, scattering amplitudes, and conformal field theory correlators emerge as distinct projections of the same underlying ensemble evolution, corresponding to equal-time, asymptotic, and symmetry-organized observables. Standard operator, diagrammatic, and path-integral formulations are recovered as computational representations of this single real-time dynamics. This organization makes explicit the distinction between fundamental dynamical structure and representational tools in QFT, and clarifies the scope within which ensemble-averaged correlators account for quantum fluctuations, while also delineating the level at which questions associated with individual realizations and randomness would arise beyond the correlator-based field-theoretic description.