Derivation of Dirac-like Effective Hamiltonian and Algebraic Statistics from Higher-Derivative Scalar Field Theory
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2026
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| _version_ | 1866901170022252544 |
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| author | Note, Masayuki |
| author_facet | Note, Masayuki |
| contents | <p>Description:</p> <p>This research article investigates the non-relativistic limit of the higher-derivative Lee--Wick (HDLW) scalar theory, formulated within a six-component Feshbach--Villars framework in Krein space.</p> <p>Building upon the operator analysis established in the preceding work (arXiv:2512.16955), this study focuses on the formal mathematical isomorphism between the HDLW scalar sector and the phenomenological Dirac theory.</p> <p><strong>Key Findings:</strong></p> <ul> <li> <p><strong>Effective Hamiltonian:</strong> By performing a Foldy--Wouthuysen expansion, the study demonstrates that the scalar theory yields a low-energy effective Hamiltonian formally identical to that of a spin-1/2 fermion.</p> </li> <li> <p><strong>Relativistic Corrections:</strong> The expansion analytically reproduces the precise coefficients of the Darwin term (<span>$\frac{e}{8m^2}\nabla\cdot\mathbf{E}$</span>) and the Thomas-corrected spin-orbit coupling.</p> </li> <li> <p><strong>Algebraic Statistics:</strong> The paper discusses how the indefinite metric of the underlying state space induces a Berry phase of <span>$\pi$</span> under adiabatic exchange, enabling the effective degrees of freedom to algebraically mimic Fermi--Dirac statistics.</p> </li> </ul> <p>This work suggests that the phenomenological properties of fermions can be understood as emergent structural features of a UV-finite bosonic theory stabilized by indefinite metric states.</p> <p>Keywords:</p> <p>Higher-Derivative Field Theory, Lee-Wick Theory, Feshbach-Villars Formalism, Krein Space, Foldy-Wouthuysen Transformation, Darwin Term, Effective Field Theory, Quantum Field Theory</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18217011 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Derivation of Dirac-like Effective Hamiltonian and Algebraic Statistics from Higher-Derivative Scalar Field Theory Note, Masayuki Quantum Field Theory High Energy Physics - Theory Mathematical Physics Lee-Wick Theory Higher-Derivative Field Theory Indefinite Metric Feshbach-Villars Formalism Krein Space Foldy-Wouthuysen Transformation Zitterbewegung Darwin Term Spin-Statistics <p>Description:</p> <p>This research article investigates the non-relativistic limit of the higher-derivative Lee--Wick (HDLW) scalar theory, formulated within a six-component Feshbach--Villars framework in Krein space.</p> <p>Building upon the operator analysis established in the preceding work (arXiv:2512.16955), this study focuses on the formal mathematical isomorphism between the HDLW scalar sector and the phenomenological Dirac theory.</p> <p><strong>Key Findings:</strong></p> <ul> <li> <p><strong>Effective Hamiltonian:</strong> By performing a Foldy--Wouthuysen expansion, the study demonstrates that the scalar theory yields a low-energy effective Hamiltonian formally identical to that of a spin-1/2 fermion.</p> </li> <li> <p><strong>Relativistic Corrections:</strong> The expansion analytically reproduces the precise coefficients of the Darwin term (<span>$\frac{e}{8m^2}\nabla\cdot\mathbf{E}$</span>) and the Thomas-corrected spin-orbit coupling.</p> </li> <li> <p><strong>Algebraic Statistics:</strong> The paper discusses how the indefinite metric of the underlying state space induces a Berry phase of <span>$\pi$</span> under adiabatic exchange, enabling the effective degrees of freedom to algebraically mimic Fermi--Dirac statistics.</p> </li> </ul> <p>This work suggests that the phenomenological properties of fermions can be understood as emergent structural features of a UV-finite bosonic theory stabilized by indefinite metric states.</p> <p>Keywords:</p> <p>Higher-Derivative Field Theory, Lee-Wick Theory, Feshbach-Villars Formalism, Krein Space, Foldy-Wouthuysen Transformation, Darwin Term, Effective Field Theory, Quantum Field Theory</p> |
| title | Derivation of Dirac-like Effective Hamiltonian and Algebraic Statistics from Higher-Derivative Scalar Field Theory |
| topic | Quantum Field Theory High Energy Physics - Theory Mathematical Physics Lee-Wick Theory Higher-Derivative Field Theory Indefinite Metric Feshbach-Villars Formalism Krein Space Foldy-Wouthuysen Transformation Zitterbewegung Darwin Term Spin-Statistics |
| url | https://doi.org/10.5281/zenodo.18217011 |