Open research questions in Quantum and Classical Electrodynamics

What the literature leaves open

• Developing a theoretical framework that remains compatible with general relativity and standard quantum field theory. Deriving the resulting stiffness-interface, phase-shift, and bound-facing signatures.

  Addendum IV to the Berg Theory · 2026 · DOI

• Reconciling discrete geometric reality with smooth continuous curves. Bridging the gap between vacuum geometry and experimental reality. Providing a set of falsifiable predictions for upcoming datasets.

  ICE CUBE PREDICTIONS AND FALSIFICATION OF RELATIVITY THROUGH THE PHI VORTEX UNI-PHI-ED REALATIVITY UFT MODEL · 2026 · DOI

• The difficulty of stabilizing global structures. The challenge of unifying various mathematical and physical systems under a single framework. The need to capture the universal structure behind local-global phenomena.

  A Dispersive Field Interpretation of Local–Global Structure · 2026 · DOI

• The Standard Model cannot explain the values of gauge couplings. The GTE framework addresses this gap by deriving gauge couplings from the arithmetic structure of the GTE polynomial.

  The Weinberg Angle, Fine-Structure Constant, and Gauge Couplings from the Polynomial · 2026 · DOI

• The paper suggests that future research should focus on constructing a mapping from the 21 vertices of Ω21 to the generators of so(4, 2) ⊕ so(4, 2). The paper also suggests that future research should investigate the implications of the topological isolation of σ = 21 for the study of dark matter.

  Two Lines Converging in One Geometry: Synthesis of Varlamov's Group-Theoretical Framework and the Ontological Fundamental Network · 2026 · DOI

• The paper identifies a gap in the existing literature, where discrete combinatorics and continuous group theory have not been synthesized to provide a unified geometric description of matter. The paper aims to address this gap by demonstrating a convergence of discrete combinatorics and continuous group theory.

  Two Lines Converging in One Geometry: Synthesis of Varlamov's Group-Theoretical Framework and the Ontological Fundamental Network · 2026 · DOI

• The study is limited to a lattice setup. The authors note that a dedicated continuum study with three or more lattice spacings is required to reduce the uncertainty. The paper is based on a specific model and may not be generalizable to other contexts.

  Induced gauge stiffness, Hopf solitons, and the consistency of an ordered vacuum: a lattice study · 2026 · DOI

• The paper identifies a gap in the understanding of the history of the magnetic monopole concept. The paper argues that the concept was not absent from quantum theory prior to Dirac's work.

  Monopoles before Dirac · 1983 · DOI

• 1. Dilaton potential from first principles. The JT dilaton potential 𝑈 (𝐴) = 4𝛽2 5𝐴2 0 3 𝐴3 is determined by requiring the sech profile to be a solution, not derived independently. A physical principle selecting this quintic-cubic form has not been identified. 𝐴5 − 2𝛽2 2. Origin of Λ. The locking strength Λ > 0 ensures quarter-turn stability and appears in the soliton mass parameter 𝛽2 = 𝑚2 + 𝜇2 + 2Λ, but is not derived from a deeper principle. 3. Free parameters. The framework contains four free parameters: 𝛼 (curvature mass scale), 𝛾𝑄 (charge coupling), Λ (locking strength), and 𝛾 (phenomenological parity-breaking detuning coupling). None are derived from first principles; all must be fixed by observation. The dimensionless ratio 𝑞/𝑀 ∼ (𝛾𝑄/𝛼) × (profile factor) isolates scale freedom in the charge-to- mass ratio. 4. Double-well conjecture. The charge emergence conjecture (Section 17) requires explicit computation of 𝑈eff(𝛿) to verify that 𝛿 = 0 is a local minimum (neutral ground state) and that minima at 𝛿 = ±𝛿∗ ≠ 0 (charged states) exist. This is the most important open calculation. 5. Mass correspondence. The relationship between 𝑀field and 𝑀𝑅 = 𝛼 ∫ |𝑅| 𝑑𝑢 is approxi- mate for the sech soliton. An analytic comparison for the explicit sech profile would clarify when they agree and to what precision. 6. Worldline reduction. The mapping from the full field theory to an effective spacetime point particle is used in Sections 11 and 15 but not derived. A complete derivation requires integrating the joint action 𝑆[𝐴(𝑥, 𝑢), Θ(𝑥, 𝑢)] over internal degrees of freedom. 7. Perfect fluid approximation. The TOV reduction in Section 19 assumes 𝑇 (4) 𝜇𝜈 takes perfect fluid form. Whether the integrated soliton stress tensor satisfies this for the explicit sech profile has not been verified. 8. Einstein–Maxwell unification. The GR embedding establishes the gravitational side. 𝜇𝜈 and 𝑗𝜇 simultaneously, Extending to the full Einstein–Maxwell system would couple 𝑇 (4) unifying mass, charge, and vortex circulation into one sourced field equation system. 9. Multi-particle interactions. The framework treats single resonances in isolation. Ex- tension to multi-particle interactions and regimes where spacetime gradients couple back to internal structure remains open. 30 10. Phase-sector classification. Whether a genuine topological invariant — winding number, Chern number, or homotopy class — can be associated with the discrete locking sectors has not been established for the localized profiles used here.

  Amplitude–Phase Geometry of Vacuum Resonances: Mass, Charge, Electromagnetic and Gravitational Coupling from Detuned Phase Structure · 2026 · DOI

• The Standard Model Lagrangian is largely postulated rather than derived. The Higgs field is introduced to break the electroweak symmetry but its potential is not derived from anything deeper.

  The Standard Model Lagrangian from the Cohesion Unified Field Theory · 2026 · DOI

• The theory is still in the development stage and requires further testing. The paper does not present experimental results to confirm the theory. The theory may have limitations in explaining certain phenomena or making predictions.

  Absolute Medium Unified Field Theory: An Axiomatic, Geometric, and Topological Framework for All Interactions · 2026 · DOI

• The gap is the lack of a single framework that explains all interactions. The gap is the lack of a unified theory that derives various equations and phenomena from a set of axioms.

  Absolute Medium Unified Field Theory: An Axiomatic, Geometric, and Topological Framework for All Interactions · 2026 · DOI

• Further development of the Berg Theory is necessary to fully understand its implications. Experimental verification of the predicted signatures is required.

  Addendum IV to the Berg Theory · 2026 · DOI

• The Standard Model of particle physics relies on 19 free parameters that must be measured rather than derived. The dynamical selection principle fixing the internal dimension N is an open problem.

  Gauge Forces and Charge Quantization from Spectral Geometry in the Dynamical Fourier Field Framework · 2026 · DOI

• To apply the 59D geometric framework to other particle masses and interactions. To further develop the No-Vacuum Principle and its implications for black hole physics and cosmology. To explore the limitations and uncertainties of the framework.

  Geometric Mass Generation in the 59-Dimensional Framework: QCD Casimir Derivation of Baryon Masses, Singularity Prevention, and Testable Predictions at the LHC · 2026 · DOI

• The Standard Model leaves open the question of its own foundations. The Standard Model provides no prediction for baryon mass ratios. Prior work has not explained why each Yukawa coupling constant takes its specific value.

  Geometric Mass Generation in the 59-Dimensional Framework: QCD Casimir Derivation of Baryon Masses, Singularity Prevention, and Testable Predictions at the LHC · 2026 · DOI

• Future research could explore the implications of the paper's approach for the measurement of the fine-structure constant. Future research could also explore the implications of the paper's approach for the understanding of other fundamental constants. Future research could investigate the connection between the fine-structure constant and other areas of physics.

  Fine-Structure Constant as a Cross-Ratio: A Geometric Reframing of α · 2026 · DOI

• The origin of the fine-structure constant remains unexplained. The standard presentation of the fine-structure constant obscures its geometric character. There is a need for a deeper understanding of the fine-structure constant's nature.

  Fine-Structure Constant as a Cross-Ratio: A Geometric Reframing of α · 2026 · DOI

• The need for a quantum-topological generalization of Resonant Vacuum Architecture. The lack of a parameter-free analytical synthesis of fundamental constants across micro, meso, and macro scales.

  Quantum Modification of Resonant Vacuum Architecture (RVA): Nonlinear Hydrodynamics of the Achromatic Singular Core and Through Spectral Synthesis of the Vacuum · 2026 · DOI

• Experimental verification of the predicted quarter-period structure. Further exploration of the geometric relation between phase closure and the fine structure constant.

  ON THE HIDDEN PHASE GEOMETRY OF PLANCK'S CONSTANT.From Maxwellian Phase Rotation to the Physical Meaning of the Photon · 2026 · DOI

• The geometric meaning of complex phase and the physical origin of quantization are not well understood. The nature of the photon and the interpretation of Planck's constant are not well understood.

  ON THE HIDDEN PHASE GEOMETRY OF PLANCK'S CONSTANT.From Maxwellian Phase Rotation to the Physical Meaning of the Photon · 2026 · DOI

• Future research could explore the implications of the global coherence constraint, - future research could investigate the detailed form of the global coherence functional C[A].

  Maxwell Theory Under a Global Coherence Constraint · 2026 · DOI

• Further study of the dodecahedral corridors of TVS23. Experimental searches for the field Ξ.

  Instantons Without Imaginary Time: The Strong CP Problem Resolved by A₅ Symmetry and the Dodecahedral Corridors of TVS23 · 2026 · DOI

• Experimental verification of the proposed model. Further investigation of the implications of the phase-topological interpretation of localization dynamics.

  CHRONAL PHOTON ROTOR THEORY · 2026 · DOI

• The physical interpretation of photon localization remains conceptually unresolved. The present work explores an alternative interpretation, treating the photon as a transient phase-ordering event.

  CHRONAL PHOTON ROTOR THEORY · 2026 · DOI

Most-cited papers in Quantum and Classical Electrodynamics

• Efficient Rotation of Local Basis Functions Using Real Spherical Harmonics · Acta Physica Polonica B · 2016 · 174 citations
• The dynamics of a charged sphere and the electron · American Journal of Physics · 1997 · 109 citations
• Multi-soliton Solutions Based on Interactions of Basic Traveling Waves with an Application to the Nonlocal Boussinesq Equation · Acta Physica Polonica B · 2016 · 30 citations
• Bottoms up: The Standard Model Effective Field Theory from a model perspective · Studies in History and Philosophy of Science Part A · 2022 · 13 citations
• Gauge invariance through gauge fixing · Studies in History and Philosophy of Science Part A · 2024 · 7 citations
• Experimental Overview on Fluctuations of Conserved Charges · Acta Physica Polonica B Proceedings Supplement · 2022 · 6 citations
• Equivalence and Duality in Electromagnetism · Philosophy of Science · 2020 · 4 citations
• The double nature of Maxwell's physical analogies · Studies in History and Philosophy of Science Part A · 2021 · 3 citations
• Nonlinear PDE Models in Semi-relativistic Quantum Physics · Computational Methods in Applied Mathematics · 2023 · 3 citations
• Ghost-free Electroweak Symmetry Breaking with Weakly Nonlocal Interactions · Acta Physica Polonica B · 2024 · 2 citations

Most recent work

• Ulianov’s Formulation of the Maxwell’s Equations, from a Spherical-Shell Electron Model · Journal of Physical Mathematics & its Applications · 2026
• Exact Green's function for fermions in an external Yang-Mills gauge field · International Journal of Modern Physics A · 2026
• Quantum Ground Theory (QGT): A Non-Linear Geometric Solution to the Vacuum Renormalization, Muon g-2 Anomaly, and the Measurement Problem · Zenodo (CERN European Organization for Nuclear Research) · 2026
• Amplitude–Phase Geometry of Vacuum Resonances: Mass, Charge, Electromagnetic and Gravitational Coupling from Detuned Phase Structure · Zenodo (CERN European Organization for Nuclear Research) · 2026
• CONSTANTS ONTOLOGY – Paper C - Recursive Physical Constants and Force Refinement in the Unified Coherence Framework Root Constants, Coupling Invariants, and the Fine-Structure Constant · Zenodo (CERN European Organization for Nuclear Research) · 2026
• Reappraisal of QED Mathematical and Physical Fundamentals · Journal of Physics & Optics Sciences · 2026
• The Standard Model Lagrangian from the Cohesion Unified Field Theory · Zenodo (CERN European Organization for Nuclear Research) · 2026
• Few-particle lepton bound states in variational approach · International Journal of Modern Physics A · 2026
• ACORN Booklet 4: The Proton · Zenodo (CERN European Organization for Nuclear Research) · 2026
• The Fundamental Constants and Interaction Laws of the Proton are Reproduced by a Mechanical Vortex Model · Zenodo (CERN European Organization for Nuclear Research) · 2026

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