I tiakina i:
| Kaituhi matua: | |
|---|---|
| Hōputu: | Recurso digital |
| Reo: | |
| I whakaputaina: |
Zenodo
2026
|
| Ngā marau: | |
| Urunga tuihono: | https://doi.org/10.5281/zenodo.20112481 |
| Ngā Tūtohu: |
Tāpirihia he Tūtohu
Kāore He Tūtohu, Me noho koe te mea tuatahi ki te tūtohu i tēnei pūkete!
|
Rārangi ihirangi:
- <p>Symplectic Active Geometrodynamics (SAGD) is developed in this volume as a regulated metric-affine and operator-theoretic framework for non-singular spacetime, spectral geometry, and emergent physical structure. The central object is the global SAGD constraint operator, constructed from metric-curvature, torsional, regulatory, and symplectic sectors. The Gauge-Equivariant Ricci Controller (GERC) provides a geometric regulatory mechanism, while the Metric-to-Torsion Channel Shift (MTCS) redirects high-curvature stress into torsional degrees of freedom. Together, these structures are proposed to stabilize geometric evolution and prevent null-volume singularities.</p> <p>Volume I establishes the foundational architecture of the theory. It begins with an axiomatic and variational formulation of SAGD, including the independent metric-affine structure, torsional sector, symplectic consistency condition, and regulated field equations. It then develops the global constraint equation and the operator formulation of the theory, including the Laplace-type structure, Dirac factorization, heat-kernel representation, spectral flow, semigroup dynamics, and the construction of the physical Hilbert space as the kernel of the SAGD operator.</p> <p>A major focus of the volume is the rigorous operator-theoretic realization of the SAGD framework. Under appropriate ellipticity, coercivity, relative boundedness, compactness, and domain assumptions, the SAGD operator admits a canonical self-adjoint realization, with the Friedrichs construction used where essential self-adjointness is not separately established. The intrinsic Dirac-type operator is introduced through the factorization of the global constraint operator, allowing the physical sector to be characterized equivalently through the Dirac kernel under suitable assumptions.</p> <p>The later chapters develop the spectral and physical consequences of this structure. These include spectral stability, near-kernel dynamics, topological protection, index-theoretic interpretation, heat-kernel geometry, holographic concentration, emergent gauge-like sectors, unitary dynamics inside the physical sector, and the algebra of physical observables. The volume concludes by positioning SAGD as a foundational operator-geometric framework for subsequent volumes on spectral physics, quantum information, measurement theory, and emergent physical phenomena.</p> <p>This work is intended as the foundational volume of a larger SAGD series. Its purpose is to define the mathematical and conceptual backbone of the theory: a regulated geometric dynamics in which spacetime, physical states, spectral observables, and emergent quantum structures are organized by a single global constraint operator and its intrinsic Dirac-geometric realization.</p>