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Coherence Fields and Path Integrals: A Correspondence for Quantum Electrodynamics

Clinton Svancara

Published Jan 1, 2026• 0 citations
Publisher

Abstract

This paper investigates whether the coherence field Rc(x, t) of Relational Field Theory (RFT) admits a correspondence whose trajectory summation is consistent with the path-integral formulation of quantum electrodynamics. We start from the RFT evolution equation for Rc, consider phase-coherent paths, and derive the effective action weighting. The analysis focuses solely on the mathematical consistency of the mapping and the conditions under which the correspondence reproduces the familiar path-integral structure. No broader interpretive or foundational claims are made.

DOI
10.17605/osf.io/j38qp

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Niels Bohr’s complementarity and Richard Feynman’s sum-over-histories are foundational to quantum mechanics, yet their unification remains elusive. Relational Field Theory (RFT) reframes these as perspectives on coherence-driven dynamics, where physical phenomena emerge from synchronized interactions modeled by the coherence field Rc(t), governed by δ R (1−Rc(t)) dt = 0, with predictions for quantum optics experiments. Complementarity arises from Rc(t) stabilizing different quantum aspects based on measurement context, while sum-over-histories reflects the aggregation of coherence pathways, analogous to Feynman’s path integral weights. Simulations (SNR = 5 to 15 dB, detectable with superconducting nanowire single-photon detectors at CERN’s Quantum Technology Initiative) validate this unification, predicting testable signatures in quantum optics experiments. Building on RFT’s derivation of the Born rule (SSRN ID [new ID]) and unification of mass, gravity, and fundamental forces (SSRN ID 5343789), this work positions RFT as a transformative framework for quantum foundations, with applications to quantum algorithm optimization for NISQ devices and collaborative opportunities at CERN. Provenance: Originally published on Zenodo (Aug 2025). 10.5281/zenodo.16790368

•Jan 1, 2025•0 citations
This paper investigates whether the coherence field Rc(x, t) of Relational Field Theory (RFT) admits a correspondence whose trajectory summation is consistent with the path-integral formulation of quantum electrodynamics. We start from the RFT evolution equation for Rc, consider phase-coherent paths, and derive the effective action weighting. The analysis focuses solely on the mathematical consistency of the mapping and the conditions under which the correspondence reproduces the familiar path-integral structure. No broader interpretive or foundational claims are made.
This paper investigates whether the coherence field Rc(x, t) of Relational Field Theory (RFT) admits a linearized phase-coherent regime that is consistent with the form of the Schr¨odinger equation. We start from the RFT evolution equation for Rc, introduce the phase-coherent condition Rc = |Rc|eiϕ(x,t), perform a linearization around a stable coherence well, and derive the correspondence to the Schr¨odinger form. The analysis focuses solely on the mathematical consistency of the mapping and the conditions under which the linearised dynamics reproduce the familiar equation. No broader interpretive or foundational claims are made.
This paper investigates whether the coherence field Rc(x, t) of Relational Field Theory (RFT) admits a phase-mode correspondence that is consistent with the gauge structure of the Maxwell equations. We start from the RFT evolution equation for Rc, note its global U(1) phase invariance, promote the symmetry to a local transformation, and derive the resulting vector field and field-strength tensor. The analysis focuses solely on the mathematical consistency of the mapping and the conditions under which the phase mode reproduces the familiar Maxwell form. No broader interpretive or foundational claims are made.
This paper investigates whether the coherence field Rc(t) of Relational Field Theory (RFT) admits a stability correspondence that is consistent with the form of the uncertainty principle. We start from the RFT evolution equation for Rc(t), identify uncertainty limits with fluctuations in coherence under measurement interactions, and show the correspondence in the high-stability limit. The analysis focuses solely on the mathematical consistency of the mapping and the conditions under which the coherence dynamics reproduce the familiar uncertainty relation. No broader interpretive or foundational claims are made.
This paper shows that the core structure of Relational Field Theory (RFT) admits a consistent variational formulation under the same minimal constraints developed in the preceding derivation. Starting from a relational action constructed to satisfy closure and measurability requirements, the operational coherence functional ( R_c = \alpha \cdot \beta \cdot \gamma ) and the persistence law ( \frac{dR_c}{dt} = -\lambda R_c + F_{int} ) re-emerge as the minimal forms compatible with collapse invariance, relational closure, measurability, and stability. The work does not claim an independent first-principles derivation; rather, it demonstrates that the established RFT core is internally consistent with a least-action-like relational structure. This strengthens the foundational coherence of the framework and provides a bridge toward deeper mathematical and geometric extensions.
We develop a coherent-field formulation of quantum electrodynamics (QED) based on coherent-state boundary conditions, in which laser fields are represented by asymptotic coherent states rather than by prescribed classical background fields. Starting from coherent-state boundary conditions and the displacement-operator formalism, we construct operator and path-integral descriptions of transitions between distinct electromagnetic coherent states. This formulation provides a coherent-field extension of conventional background-field QED and incorporates the quantum dynamics of the coherent field itself. The corresponding path-integral representation contains a functional integral over coherent-field histories in addition to the usual functional integral over quantum fluctuations, thereby extending the conventional background-field description. The resulting path-integral representation naturally leads to an effective action for the stationary coherent-field configuration. The corresponding saddle-point condition yields an effective Maxwell equation containing contributions from vacuum polarization, photon fluctuations, and coherent-field fluctuations. In the limit where the latter two contributions vanish, the formalism reduces to the conventional Heisenberg-Euler description.
Niels Bohr’s complementarity and Richard Feynman’s sum-over-histories are foundational to quantum mechanics, yet their unification remains elusive. Relational Field Theory (RFT) reframes these as perspectives on coherence-driven dynamics, where physical phenomena emerge from synchronized interactions modeled by the coherence field Rc(t), governed by δ R (1−Rc(t)) dt = 0, with predictions for quantum optics experiments. Complementarity arises from Rc(t) stabilizing different quantum aspects based on measurement context, while sum-over-histories reflects the aggregation of coherence pathways, analogous to Feynman’s path integral weights. Simulations (SNR = 5 to 15 dB, detectable with superconducting nanowire single-photon detectors at CERN’s Quantum Technology Initiative) validate this unification, predicting testable signatures in quantum optics experiments. Building on RFT’s derivation of the Born rule (SSRN ID [new ID]) and unification of mass, gravity, and fundamental forces (SSRN ID 5343789), this work positions RFT as a transformative framework for quantum foundations, with applications to quantum algorithm optimization for NISQ devices and collaborative opportunities at CERN. Provenance: Originally published on Zenodo (Aug 2025). 10.5281/zenodo.16790368