Quantum mechanics provides one of the most accurate mathematical descriptions of Nature, successfully explaining interference, superposition, entanglement, quantum measurement, and the dynamics of microscopic systems. Despite its remarkable predictive success, the physical origin of quantum coherence and the interpretation of wavefunction collapse remain subjects of ongoing debate, leading to numerous interpretations including the Copenhagen interpretation, decoherence theory, the many-worlds interpretation, relational quantum mechanics, and QBism. In this work we propose Green-Function Architecture Theory (GFAT) as a structural framework underlying the conventional Hilbert-space formulation of quantum mechanics. Rather than modifying the mathematical formalism of quantum theory, GFAT introduces a deeper structural level based upon interacting Green functions and their associated diagram spaces. Within this framework, quantum coherence is proposed to be a property of connected Green-function architectures, while wavefunctions are interpreted as effective Hilbert-space representations reconstructed from these architectures. The framework introduces three structural principles: the Architecture Coherence Principle, the Architecture Representation Principle, and the Architecture Conservation Principle. These principles provide a unified structural interpretation of quantum interference, measurement, decoherence, geometric phases, entanglement, bound states, and particle stability. Existing interpretations of quantum mechanics are not regarded as competing descriptions but as complementary mathematical layers representing the same underlying physical reality. The present work therefore proposes a structural foundation of quantum physics in which Green-function architectures provide the underlying organizational principle from which quantum phenomena emerge while leaving
Quantum mechanics provides one of the most accurate mathematical descriptions of Nature, successfully explaining interference, superposition, entanglement, quantum measurement, and the dynamics of microscopic systems. Despite its remarkable predictive success, the physical origin of quantum coherence and the interpretation of wavefunction collapse remain subjects of ongoing debate, leading to numerous interpretations including the Copenhagen interpretation, decoherence theory, the many-worlds interpretation, relational quantum mechanics, and QBism. In this work we propose Green-Function Architecture Theory (GFAT) as a structural framework underlying the conventional Hilbert-space formulation of quantum mechanics. Rather than modifying the mathematical formalism of quantum theory, GFAT introduces a deeper structural level based upon interacting Green functions and their associated diagram spaces. Within this framework, quantum coherence is proposed to be a property of connected Green-function architectures, while wavefunctions are interpreted as effective Hilbert-space representations reconstructed from these architectures. The framework introduces three structural principles: the Architecture Coherence Principle, the Architecture Representation Principle, and the Architecture Conservation Principle. These principles provide a unified structural interpretation of quantum interference, measurement, decoherence, geometric phases, entanglement, bound states, and particle stability. Existing interpretations of quantum mechanics are not regarded as competing descriptions but as complementary mathematical layers representing the same underlying physical reality. The present work therefore proposes a structural foundation of quantum physics in which Green-function architectures provide the underlying organizational principle from which quantum phenomena emerge while leaving
Quantum coherence lies at the heart of quantum mechanics and underlies interference, entanglement, and quantum information. Within conventional quantum theory, coherence is mathematically represented by the wavefunction or, more generally, by the off-diagonal elements of the density matrix. Although this formalism predicts experimental observations with extraordinary precision, the physical origin of coherence and its apparent disappearance during measurement continue to motivate diverse interpretations, including the Copenhagen interpretation, decoherence theory, many-worlds, relational quantum mechanics, and QBism. In the present work we propose a complementary structural interpretation based on Green-Function Architecture Theory (GFAT). Rather than considering quantum coherence to be a primitive property of the wavefunction, we propose that coherence is fundamentally a property of connected Green-function architectures represented by diagram spaces. The wavefunction is interpreted as an effective Hilbert-space representation of an underlying Green-function architecture. Within this framework, quantum interference arises from architecture coherence associated with a common holonomy, whereas measurement corresponds to an architecture transformation that redistributes coherence without destroying it. Consequently, wavefunction collapse is interpreted as an emergent description of a deeper structural process occurring within the underlying Green-function architecture. The proposed framework leaves the mathematical predictions of quantum mechanics completely unchanged while suggesting a deeper structural origin for quantum coherence, interference, and measurement. The double-slit experiment is discussed as the first physical application of this architecture-based interpretation.
Modern theoretical physics is formulated through several highly successful mathematical frameworks. Green functions describe propagation, Hilbert spaces provide the mathematical language of quantum mechanics, gauge theories describe transport and symmetry, quantum field theory combines relativistic fields with quantum mechanics, and statistical mechanics relates microscopic dynamics to thermodynamic observables. Although these theories employ different primitive mathematical structures, they exhibit remarkable mathematical compatibility. The structural origin of this compatibility remains largely unexplained. The purpose of this paper is to investigate whether these apparently distinct frameworks admit a common mathematical description. We introduce the Architecture Principle, according to which the primitive mathematical object is a Green-Function Architecture rather than an isolated Green function, Hilbert space, quantum state, or particle. Green functions, Hilbert-space representations, gauge transport, quantum field theoretic propagators, and statistical ensembles are interpreted as different representations of a common underlying architecture. The associated Architectural Multiplicity provides a structural invariant that organizes these representations within a unified mathematical framework. The present work should be viewed as a structural reconstruction program rather than a replacement for established physical theories. Existing mathematical formalisms remain unchanged; the Architecture Principle instead proposes a common structural foundation that explains their mathematical coherence. The paper develops the basic definitions, introduces the principal architectural invariant, formulates the Representation Principle, discusses applications to several branches of theoretical physics, and identifies the principal mathematical problems that remain open.
Quantum theory and quantum field theory are traditionally formulated using Hilbert spaces, differential operators, Green functions, and gauge fields. Although these mathematical structures have been remarkably successful, they are usually introduced independently. The present article summarizes a research program whose objective is to identify a common structural origin underlying these apparently distinct mathematical frameworks. The central proposal is that interacting Green functions should be classified according to the topology and architecture of their associated diagram spaces rather than solely through their analytical properties. This leads to Green-Function Architecture Theory (GFAT), in which Green functions generate diagram spaces admitting homological classification, primitive architecture generators, architecture coordinates, and a proposed Green-Function Architecture Master Theorem. A complementary geometric program introduces coherence manifolds and holonomy geometry, suggesting that Hilbert spaces and quantum states may emerge from an underlying coherence geometry. Together, these developments outline a unified structural framework connecting Green functions, topology, geometry, and quantum theory. The present article summarizes the mathematical foundations, current achievements, and remaining open problems of this research program.
Modern theoretical physics is formulated through several highly successful mathematical frameworks, including Green-function theory, quantum mechanics, quantum field theory, gauge theory and statistical mechanics. Although these theories employ different mathematical objects and were developed independently, they exhibit remarkable mathematical compatibility. Green functions naturally appear in quantum field theory, Hilbert-space methods underlie quantum mechanics, gauge theories are formulated geometrically, and statistical mechanics connects microscopic dynamics with macroscopic thermodynamics. The mathematical origin of this compatibility remains an open conceptual question. This paper investigates whether these apparently different frameworks can be understood as representations of a common underlying mathematical structure. We introduce the Architecture Principle, according to which the primitive object is not a Green function, wave function or Hilbert space, but a Green-Function Architecture describing propagation, interaction, closed transport and structural consistency. Green functions, quantum-mechanical states, gauge transport and statistical ensembles are interpreted as different mathematical representations of the same underlying architecture. The proposed framework does not modify the established equations of physics. Instead, it provides a common structural language that relates several major branches of theoretical physics while preserving their existing mathematical formalisms. The paper develops the basic concepts of the Architecture Principle, introduces an architectural invariant, formulates the Representation Principle and discusses representative applications. Finally, the principal mathematical problems required for a complete representation theory are identified.
Modern theoretical physics relies on Green functions, Hilbert spaces, quantum mechanics, quantum field theory, gauge theory, particle physics, and statistical mechanics. Although these frameworks were developed for different purposes, they fit together with remarkable mathematical coherence. This paper proposes the Architecture Principle, according to which the primitive object is not the wave function, Hilbert space, particle, or isolated Green function, but a Green-Function Architecture describing propagation, interaction, holonomy, and recursive closure. The central invariant of such an architecture is the Architectural Multiplicity, which organizes the reconstruction of energy, mass, quantum phase, entropy, statistical ensembles, Green functions, and Hilbert-space representations. The framework does not replace established theories; rather, it proposes a common structural origin explaining why their mathematical formalisms fit together naturally.
Modern theoretical physics employs several fundamental mathematical structures, including Green functions, Hilbert spaces, operator algebras, Gibbs ensembles, gauge fields, and spacetime geometry. These structures are traditionally introduced independently and serve as separate foundations for quantum mechanics, quantum field theory, statistical mechanics, and general relativity. In the present work, we propose an alternative mathematical organization based on a single Reconstruction Principle. Beginning with one primitive mathematical architecture, successive reconstruction layers generate transport operators, Green functions, Diagram Hilbert Spaces, complex quantum operators, Gibbs ensembles, entropic projections, and finally macroscopic spacetime together with gauge fields. Each layer is reconstructed uniquely from its predecessor without introducing additional primitive mathematical structures. Consequently, Hilbert space, Green functions, and spacetime are interpreted as successive mathematical representations of one underlying architecture rather than independent foundations. The resulting reconstruction hierarchy provides a unified conceptual framework connecting quantum mechanics, statistical mechanics, gauge theory, and emergent gravity while substantially reducing the number of independent assumptions.