Symplectic Active Geometrodynamics III The Global Constraint Equation and Operator Formulation
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2026
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| _version_ | 1866901113923436544 |
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| author | Heydari, Hoshang |
| author_facet | Heydari, Hoshang |
| contents | <p>We present an operator formulation of Symplectic Active Geometrodynamics (SAGD), providing a unified and structurally complete representation of the theory.</p> <p>Building on the axiomatic foundations and variational structure developed in previous works, we introduce a global constraint operator acting on the geometric configuration space. Physical states are defined as elements of the kernel of this operator, establishing SAGD as a constrained geometric system with a well-defined spectral structure.</p> <p>This formulation reveals that the symplectic information constraint, metric-affine dynamics, and geometric regulation mechanism (GERC) can be consistently encoded within a single operator framework. The resulting structure provides a natural bridge between geometric evolution, constraint dynamics, and spectral representations of spacetime.</p> <p>We argue that the operator formulation represents the fundamental description of SAGD, with the previously derived field equations emerging as its classical limit. This work establishes the operator-level formulation of SAGD as the fundamental description of the theory.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19335222 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Symplectic Active Geometrodynamics III The Global Constraint Equation and Operator Formulation Heydari, Hoshang <p>We present an operator formulation of Symplectic Active Geometrodynamics (SAGD), providing a unified and structurally complete representation of the theory.</p> <p>Building on the axiomatic foundations and variational structure developed in previous works, we introduce a global constraint operator acting on the geometric configuration space. Physical states are defined as elements of the kernel of this operator, establishing SAGD as a constrained geometric system with a well-defined spectral structure.</p> <p>This formulation reveals that the symplectic information constraint, metric-affine dynamics, and geometric regulation mechanism (GERC) can be consistently encoded within a single operator framework. The resulting structure provides a natural bridge between geometric evolution, constraint dynamics, and spectral representations of spacetime.</p> <p>We argue that the operator formulation represents the fundamental description of SAGD, with the previously derived field equations emerging as its classical limit. This work establishes the operator-level formulation of SAGD as the fundamental description of the theory.</p> |
| title | Symplectic Active Geometrodynamics III The Global Constraint Equation and Operator Formulation |
| url | https://doi.org/10.5281/zenodo.19335222 |