Framework

This page collects the current AWS research stack, grouped into four layers (conceptual / ontological, mathematical, operational / measurement theory, and phenomenology), followed by pedagogical works.

Layer 0 – Conceptual foundations

• AWS-Phase: A conceptual entry point to AWS that reinterprets quantum behaviour through the geometry of accumulated action. Action is taken as primary and defines the coordinates of a four-dimensional manifold, with scalar phase evolving over this space and energy–momentum emerging as gradients of action rather than inputs. Quantization is traced to global phase coherence around closed geodesics, making interference, discreteness, and dynamics consequences of scalar geometry. The paper provides the conceptual and geometric foundation for the more technical AWS modules. Paper: On the Quantum Nature of Action and Phase.
• AWS-Ontology: Explores the ontological reading of AWS: what is taken as physically real, and how familiar objects such as particles, fields, and spacetime events arise as coarse-grained descriptors of a single scalar phase and its quantized flux. The paper develops an operational account of spacetime as an emergent label space for equivalence classes of AWS events, clarifies the status of probabilities and measurement outcomes in terms of retarded projection kernels, and compares the AWS ontology to more traditional realist and operationalist views in quantum foundations. It is intended as a bridge between the conceptual picture of AWS-Phase and the more technical framework and module papers. Paper: Action–Wave Space and the Operational Emergence of Spacetime (in preparation; Zenodo preprint forthcoming).

Layer 1a – Mathematical infrastructure

• AWS-Geometry-I: Develops a geometric framework in which a single null eikonal phase \(\Phi\) and its phase–flux current \(\Omega_{\mathrm{cur}} = d(d\Phi)\) on a globally hyperbolic Lorentzian four-manifold \((M,g)\) induce a Lorentzian–symplectic structure on the defect-free region \(M^{\circ}\). It proves that, under mild cohomological assumptions, the phase and flux data uniquely fix (up to conformal rescaling and symplectomorphism) a Lorentzian conformal class \([g]\) and a compatible symplectic form \(\Omega\), together with a torsion-free Weyl connection \(\nabla^{W}\) satisfying \(\nabla^{W} g = 2Q \otimes g\) and \(\nabla^{W} \Omega = 0\). On the Hamilton–Jacobi side, \(\Phi\) defines an exact Lagrangian graph in \(T^{*}M^{\circ}\) and yields Bohr–Sommerfeld-type quantization conditions from the integral class \([\Omega/(2\pi\hbar)]\). In the AWS programme this paper provides the common Lorentzian–symplectic background and compatible connection used by AWS-Fiber and AWS-Kernel, and ultimately in the AWS-Framework synthesis. Paper: Phase-induced Lorentzian–symplectic geometry and Hamilton–Jacobi polarization (Under review per 9-12-2025, J. Geom. Phys.).
• AWS-Fiber: Analyses compact, oriented four-manifolds with fixed integral cohomology classes and quadratic curvature functionals. A scale-invariant variational principle is used to strongly restrict the allowed topologies, isolating a narrow class of manifolds with Euler characteristic \(\chi = 2\), second Betti number \(b_2 = 3\), and a small set of admissible intersection forms. These results give a topology-selection mechanism for internal configuration spaces that are both topologically stable and compatible with quantized flux sectors and nontrivial holonomy. Within these justify the formation of compact “scalartons” used in AWS-Framework and other AWS papers. Paper: Topology selection on compact four-manifolds under integral cohomology constraints (Submitted, Differ. Geom. Appl.).
• AWS-Kernel: Develops the microlocal and operator-theoretic backbone of the AWS projection mechanism by treating the causal projector as a Fourier-integral operator on a globally hyperbolic spacetime with compact internal fibers. Under Hadamard-type assumptions the associated Gram operator \(K = \Pi^{\dagger}\Pi\) is shown to be an elliptic pseudodifferential operator of order zero with principal symbol one, so that \(\Pi\) acts as an approximate isometry and \(K = I + R\) with a controlled order-\(-1\) remainder. These results are model-independent yet, in AWS-Framework, supply the rigorous foundation for viewing the projector as a near-unitary, flux-preserving map from internal fibers to spacetime. They underpin both the Born push-forward relation and the measurement dynamics developed in AWS-Measurement. Paper: Projection kernels for parameter-dependent hyperbolic operators on globally hyperbolic Lorentzian manifolds (In preparation).

Layer 1b – Mathematical synthesis

• AWS-Framework: Formulates the AWS programme as a single, non-circular framework based on one physical postulate (Action primacy) and a small set of geometric and analytic primitives. From these it shows that a single scalar phase and its quantized flux induce a Lorentzian–symplectic structure with a compatible Weyl connection, that compact “AWS domains” selected by a scale-invariant curvature+flux functional have Betti data (χ, b₁, b₂) = (2, 1, 3) and assemble into a smooth fibration π: M → M₄, and that a parameter-dependent retarded projection yields an almost-isometric map with an emergent Born/POVM structure and an infrared limit described by general relativity and quantum field theory on (M₄, g₄). The paper states an explicit “AWS framework theorem” summarizing this derivation chain from Action primacy to infrared GR+QFT and clarifies which ingredients are assumptions and which are derived. Paper: Foundations of Action–Wave Space (AWS): Lorentzian–Symplectic Geometry, Topology Selection, and Infrared QFT (In preparation; Zenodo preprint forthcoming).

Layer 2 – Operational & dynamics

• AWS-Measurement: Develops a model-independent measurement framework in which a single causal projection operator with a retarded kernel on a compact internal configuration space generates both POVMs and quantum instruments. Born probabilities are recovered as push-forward measures of an approximate isometry, while a strictly convex stability functional yields deterministic outcome selection and effective collapse dynamics. The formalism predicts four universal, experimentally testable scaling laws governing collapse time, visibility decay, deviations from ideal Born statistics, and rotated-basis transfer curves. It is particularly suited to continuous weak-measurement platforms such as circuit QED, optomechanics, and photonic experiments. Paper: Measurement probabilities and outcome selection from causal projection kernels (Under review per 26-11-2025, J. Phys. A.).
• AWS-QG-I: Develops a scalar-field-based approach to quantum gravity in which metric–symplectic compatibility and topological phase coherence replace canonical operator quantization. The Einstein field equations and a natural curvature bound \(|R| \lesssim \hbar^{-2}\) arise from the scalar wave dynamics on the AWS manifold, yielding classical general relativity as an effective description in the appropriate limit. A causal projection mechanism then defines observables and leads to concrete predictions for cosmology, gravitational-wave propagation, and high-curvature regimes. This work positions AWS as a UV-finite, background-independent candidate theory of quantum gravity. Paper: Quantum Gravity from Action-Wave Space: Curvature, Quantization, and Causal Projection.

Layer 3 – Phenomenology & sectors

• AWS-SM: Derives the complete Standard Model Lagrangian as the low-energy projection of a single scalar phase field in AWS. The fixed fiber topology \((\chi, b_1, b_2) = (2, 1, 3)\) uniquely selects the gauge group \(\mathrm{SU}(3)_C \times \mathrm{SU}(2)_L \times \mathrm{U}(1)_Y\), three fermion generations, and a complex Higgs doublet. Yukawa couplings arise as geometric overlap integrals on the fiber, providing an explanation for mass hierarchies, mixing patterns, and CP phases in terms of scalar geometry rather than free parameters. This paper positions AWS as a concrete, predictive candidate for a first-principles origin of the Standard Model. Paper: The Standard Model from Action–Wave Space.
• AWS-Entropy: Reproduces the Bekenstein–Hawking area law and its logarithmic corrections within the AWS framework. Black-hole entropy is computed in three equivalent ways—as a Wald–Noether charge, as a flux-sector microstate count, and as an entanglement entropy of the projection—and in each case yields \(S = A / (4 G \hbar) – (3/2)\ln A + \cdots\). No UV regulators or extra fields are required; finiteness follows from the fixed fiber topology with \((\chi, b_2) = (2, 3)\). The work demonstrates how quantum gravity and black-hole thermodynamics can emerge from scalar phase geometry alone. Paper: Black-Hole Entropy from Scalar Phase Geometry.
• AWS-H: Derives the hydrogen spectrum from AWS, including Bohr levels, Dirac fine structure, and leading radiative and hyperfine corrections. Discrete energy levels appear as interference-stable scalar modes selected by phase quantization and Maslov indices on closed geodesics in action space. Spin-½ holonomy reproduces the Dirac spectrum, while finite curvature and projection effects naturally generate Lamb-shift-like corrections without ad hoc renormalization. The paper serves as a key benchmark showing that AWS matches precision atomic data while retaining a geometric, operator-free formulation. Paper: Hydrogen Spectrum from Action–Wave Space.

Older (Pedagogical) works:

• Derivations from Action-Wave Space I: Operator-Free Quantization and the Schrodinger Equation Introduces the AWS framework through a derivation of non-relativistic quantum mechanics without operator postulates. Phase coherence constraints on scalar fields and topological quantization on action-space geodesics are used to obtain the Schrödinger equation and canonical structures. This recasts standard quantum mechanics as an emergent description of scalar phase geometry rather than an axiomatically independent theory. It serves as a pedagogical bridge between introductory AWS concepts and more advanced technical papers. Paper: Derivations from Action-Wave Space I: Operator-Free Quantization and the Schrodinger Equation.
• Derivations from Action-Wave Space II: Dirac and Klein–Gordon Equations from Phase Geometry Extends the AWS formalism to relativistic quantum mechanics by deriving the Dirac and Klein–Gordon equations from a single scalar phase field on a Lorentzian–symplectic manifold. The causal structure, spinor dynamics, and mass shells are shown to arise from topological coherence and scalar phase transport, with spinor degrees of freedom emerging from holonomy rather than being postulated. The work provides a unified geometric origin for relativistic wave equations within AWS and prepares the ground for later treatments of spin, statistics, and field quantization. Paper: Derivations from Action-Wave Space II: Dirac and Klein–Gordon Equations from Phase Geometry.
• Derivations from Action-Wave Space III: The Quantum Harmonic Oscillator Applies AWS to the quantum harmonic oscillator, deriving its full energy spectrum from interference-stable scalar modes on closed geodesics. The familiar \((n + 1/2)\hbar\omega\) levels emerge from Maslov indices and phase-winding constraints rather than ladder operators. This example demonstrates how AWS reproduces textbook results using geometric quantization alone. It offers a clear and calculable test case linking AWS to standard quantum mechanics. Paper: Derivations from Action-Wave Space III: The Quantum Harmonic Oscillator.
• Derivations from Action-Wave Space IV: The Hydrogen Atom from Phase Quantization and Scalar Projection – Extends the AWS approach to the hydrogen atom, deriving discrete energy levels and orbital structure from topological phase quantization in action space. The usual quantum numbers \(n\), \(\ell\), and \(m\) arise from winding constraints on radial and angular geodesics, and projection explains the emergence of familiar real-space orbitals. Without invoking a potential in configuration space or operator quantization, AWS reproduces the hydrogen spectrum from scalar geometry. This paper anticipates and complements the more complete AWS-H treatment of the hydrogen spectrum. Paper: Derivations from Action-Wave Space IV: The Hydrogen Atom from Phase Quantization and Scalar Projection.