Scale-Dependent Unification of Statistics and Dynamics: Emergence of the Dirac Field from a Scalar Progenitor (Part IV)
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2026
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| _version_ | 1866901693512286208 |
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| author | Note, Masayuki |
| author_facet | Note, Masayuki |
| contents | <p>We present a unified framework where the foundational structures of the Standard Model—Dirac like spinors, Abelian gauge interactions, and Fermi statistics—emerge not as independent postulates, but as necessary geometric consequences of a single higher-derivative scalar Lagrangian. Building on our preceding work regarding ultraviolet uniqueness (Part I), algebraic onsistency (Part II), and the emergent Born rule (Part III), we utilize the six-component Feshbach-Villars formalism as a bridge between the Lee-Wick scale (M ≈ 11.3 TeV) and low-energy physics. By analyzing this dynamics within a Split-Quaternionic Krein space, we derive the non-relativistic limit via a generalized Foldy-Wouthuysen transformation, reproducing the Darwin term with its precise coefficient (1/8m2). Furthermore, we identify the gauge field as an emergent Berry connection and demonstrate that the Pauli exclusion principle originates from the topological π-Berry phase inherent to the underlying geometry. Crucially, this framework implies a scale-dependent transmutation of statistics: the system behaves as a fermion in the infrared effective limit, while asymptotically restoring its fundamental bosonic scalar nature in the ultraviolet limit, suggesting a radical unification of matter and force.</p> <ul> <li>v1.01 Section "VI. PHENOMENOLOGICAL IMPLICATIONS AND PRECISION TESTS" has been added.</li> <li>v1.02 "Universal Shift in Higgs Couplings" has been added.</li> </ul> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18512263 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Scale-Dependent Unification of Statistics and Dynamics: Emergence of the Dirac Field from a Scalar Progenitor (Part IV) Note, Masayuki Higher-Derivative Field Theory Lee-Wick Theory Scalar Field Emergent Spinors Matter-Force Unification Split-Quaternions Six-Component Formalism Feshbach-Villars Formalism Foldy-Wouthuysen Transformation Indefinite Metric (Krein Space) <p>We present a unified framework where the foundational structures of the Standard Model—Dirac like spinors, Abelian gauge interactions, and Fermi statistics—emerge not as independent postulates, but as necessary geometric consequences of a single higher-derivative scalar Lagrangian. Building on our preceding work regarding ultraviolet uniqueness (Part I), algebraic onsistency (Part II), and the emergent Born rule (Part III), we utilize the six-component Feshbach-Villars formalism as a bridge between the Lee-Wick scale (M ≈ 11.3 TeV) and low-energy physics. By analyzing this dynamics within a Split-Quaternionic Krein space, we derive the non-relativistic limit via a generalized Foldy-Wouthuysen transformation, reproducing the Darwin term with its precise coefficient (1/8m2). Furthermore, we identify the gauge field as an emergent Berry connection and demonstrate that the Pauli exclusion principle originates from the topological π-Berry phase inherent to the underlying geometry. Crucially, this framework implies a scale-dependent transmutation of statistics: the system behaves as a fermion in the infrared effective limit, while asymptotically restoring its fundamental bosonic scalar nature in the ultraviolet limit, suggesting a radical unification of matter and force.</p> <ul> <li>v1.01 Section "VI. PHENOMENOLOGICAL IMPLICATIONS AND PRECISION TESTS" has been added.</li> <li>v1.02 "Universal Shift in Higgs Couplings" has been added.</li> </ul> |
| title | Scale-Dependent Unification of Statistics and Dynamics: Emergence of the Dirac Field from a Scalar Progenitor (Part IV) |
| topic | Higher-Derivative Field Theory Lee-Wick Theory Scalar Field Emergent Spinors Matter-Force Unification Split-Quaternions Six-Component Formalism Feshbach-Villars Formalism Foldy-Wouthuysen Transformation Indefinite Metric (Krein Space) |
| url | https://doi.org/10.5281/zenodo.18512263 |