Introduction

Action-Wave Space (AWS) is a first-principles theory in which all matter, forces, and spacetime emerge from a single real scalar field \(\Phi(S^\mu)\) defined on a four-dimensional Lorentzian symplectic manifold \(\mathscr{M}_{\text{AWS}}\). The coordinates \(S^\mu = \left( \int p_x dx,\ \int p_y dy,\ \int p_z dz,\ \int E dt \right)\) represent intrinsic action variables and form the fundamental geometry of physical law—spacetime emerges only as a projection. The scalar field determines both the metric \(g_{\mu\nu}(S)\) and symplectic structure \(\Omega_{\mu\nu}(S) = 2 \nabla_{[\mu} \partial_{\nu]} \Phi\), and evolves according to a covariant variational principle \(\nabla^\mu \nabla_\mu \Phi = 0\). Quantization arises from topological phase coherence on closed loops: \(\oint \partial_\mu \Phi \, dS^\mu = 2\pi n\hbar\). Observable fields \(\psi(x)\) in emergent spacetime arise via causal projection \(\pi: \mathscr{M}_{\text{AWS}} \to M_4\) through a scalar-derived kernel \(G_R(x, S)\). Each spacetime point \(x^\mu\) corresponds to a compact domain \(D_x = \pi^{-1}(x)\)—called a scalarton—with fixed topological structure \((\chi, b_1, b_2) = (2,1,3)\). These scalartons enforce interference stability and flux quantization, giving rise to spin, statistics, generation structure, and the spacetime metric as emergent features of scalar phase geometry.

Foundations:

• AWS: A Topological Theory of Pre-Spacetime Quantum Gravity from Scalar Phase Geometry – This paper serves as the foundation of AWS theory. It derives fermion spin, anti-commutation, and the three-generation structure of matter from a single real scalar field defined on a curved Lorentzian symplectic manifold. Observable amplitudes arise via causal projection from compact domains with fixed topology \((\chi, b_1, b_2) = (2, 1, 3)\), enforcing scalar phase coherence, quantized symplectic flux, and curvature regularity. The Clifford algebra, Dirac equation, and Pauli exclusion principle emerge from scalar flux braiding and Möbius-type holonomy. The paper provides the foundational, first-principles derivations of the projection kernel, the metric–symplectic compatibility condition, and the topological constraints necessary for interference-stable quantization. It also predicts testable effects such as curvature-induced Pauli violation and gravitational modulation of entanglement entropy—offering a unified scalar foundation for fermionic matter and quantum gravity. Paper: AWS: A Topological Theory of Pre-Spacetime Quantum Gravity from Scalar Phase Geometry.
• On the Quantum Nature of Action and Phase – This paper reinterprets quantum behavior through the geometry of accumulated action and forms the conceptual foundation of AWS theory. It introduces a new perspective in which action is not derived from motion, but defines the coordinates of a four-dimensional manifold. Scalar phase evolves over this manifold, and energy and momentum emerge as gradients of action-space, not inputs. Quantization arises from global phase coherence around closed geodesics, making interference, discreteness, and dynamics consequences of scalar geometry. This work provides the conceptual and geometric foundation for the AWS framework. Paper: On the Quantum Nature of Action and Phase.
• Topological Quantization and the Geometry of Scalartons in Action-Wave Space – This paper introduces and formalizes the concept of scalartons as topologically quantized, interference-stable wave structures in AWS. These excitations arise from scalar holonomy in regions with fixed topological structure \((\chi, b_1, b_2) = (2,1,3)\), forming a geometric analog to instantons and geons. The work lays the foundation for interpreting matter as stable phase-quantized vortex sectors in a scalar-only theory. Paper: Topological Quantization and the Geometry of Scalartons in Action-Wave Space.
• Wavefunction Collapse, the Born Rule, and Bell Correlations from Scalar Projection Geometry in Action-Wave Space – This paper derives wavefunction collapse, probabilistic amplitudes, and Bell correlations directly from the scalar geometry of AWS. Collapse is shown to emerge as a deterministic relaxation process governed by curvature-filtered projection of phase gradients. The Born rule follows from interference-stable phase transport, and Bell inequality violations arise from scalar holonomy—without invoking nonlocality, operators, or stochastic dynamics. Paper: Wavefunction Collapse, the Born Rule, and Bell Correlations from Scalar Projection Geometry in Action-Wave Space.

Extensions:

• Emergence of SU(3) Gauge Symmetry from Scalar Phase Geometry in Action-Wave Space – This paper shows how SU(3) gauge symmetry, including structure constants and confinement, arises from triple-overlap flux sectors on a symplectic manifold. The full QCD gauge structure is derived from scalar curvature and symplectic holonomy without invoking internal symmetries or gauge fields. Larger groups like SU(5) are excluded by topological constraints, explaining the uniqueness of SU(3). Paper: Emergence of SU(3) Gauge Symmetry from Scalar Phase Geometry in Action-Wave Space.
• Quantum Gravity from Action-Wave Space: Curvature, Quantization, and Causal Projection – AWS provides a scalar-field-based derivation of quantum gravity, replacing operator quantization with topological phase coherence and metric–symplectic compatibility. The Einstein field equations and a curvature bound \(|R| \lesssim \hbar^{-2}\) arise naturally from scalar wave dynamics. A causal projection mechanism yields classical observables and predicts testable effects in cosmology and gravitational wave physics. Paper: Quantum Gravity from Action-Wave Space: Curvature, Quantization, and Causal Projection.

Older works:

• Derivations from Action-Wave Space I: Operator-Free Quantization and the Schrodinger Equation – This paper introduces the AWS framework through a foundational derivation of non-relativistic quantum mechanics. By replacing operator algebra with phase coherence constraints on scalar fields, the Schrödinger equation and canonical structures emerge from topological quantization. It sets the stage for a geometry-based understanding of quantum theory without invoking Hilbert space axioms. 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 – This work extends the AWS formalism to relativistic quantum mechanics by deriving the Dirac and Klein–Gordon equations from a 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. It provides a unified geometric origin for relativistic wave equations without spinor postulates. 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 – The energy spectrum of the quantum harmonic oscillator is derived exactly from AWS principles, using interference-stable scalar wave modes on closed geodesics. This paper demonstrates how AWS reproduces textbook results from geometric quantization alone, without operator methods. It serves as a key pedagogical link between the AWS framework and canonical 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 – This paper derives the discrete energy levels and orbital structure of the hydrogen atom from topological phase quantization in action space. The usual quantum numbers \(n\), \(\ell\), and \(m\) emerge from winding constraints on radial and angular geodesics. Without using a potential or operator quantization, AWS reproduces the hydrogen spectrum and explains projection into real-space orbitals. Paper: Derivations from Action-Wave Space IV: The Hydrogen Atom from Phase Quantization and Scalar Projection.
• Action-Wave Space: A First-Principles Approach to Quantum Theory, Relativity, and Gauge Fields – Introduces the AWS manifold and derives quantum mechanics, general relativity, and the Standard Model gauge group from a unified geometric wave equation. Projection from action-space to spacetime recovers observables and classical dynamics. Paper: https://doi.org/10.5281/zenodo.14989103.