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The Architecture Principle Green-function Architectures, Architectural Multiplicity, and the Reconstruction of Quantum Physics

Borros Arneth

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.2139/ssrn.7053298

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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.

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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.

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The General Principles of Quantum Theory

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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 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.