Complex Time and the Unification of Quantum, Thermal, and Geometric Degrees of Freedom A First-Principles Derivation
Fuente:
Zenodo
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Recurso digital |
| Lenguaje: | inglés |
| Publicado: |
Zenodo
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866901067088789504 |
|---|---|
| author | li, yuanjian |
| author_facet | li, yuanjian |
| contents | <p>We present a first-principles derivation of a unified field theory that combines quantum dynamics, thermal field theory, and two-dimensional quantum gravity within a single holomorphic framework. The fundamental object is a complex time manifold $\mathcal{M}$---a compact Riemann surface with local coordinate $z = \tau/\ell_P + i t/\ell_P$, where $\ell_P$ is the Planck time. The quantum state is a holomorphic section $\Psi(z)$ of a line bundle over $\mathcal{M}$, and the geometry is encoded in a K\"ahler metric $ds^2 = \Omega^2(z,\bar{z})\,dz d\bar{z}$. Starting from the principle of least action, general covariance on $\mathcal{M}$, and the correspondence principle, we construct the total action $S = S_{\text{EH}} + S_{\text{matter}} + S_{\text{int}}$. Variation yields a coupled system: a modified wave equation for $\Psi$ that reduces to the Schr\"odinger equation in the flat limit, and a Liouville equation for $\Omega$ that encodes the feedback of quantum information on geometry. The KMS condition emerges as a natural boundary condition from the compactification of the imaginary time direction. We show that in the semi-classical limit, the theory reproduces the thermodynamics of black holes and predicts a fundamental decoherence mechanism with rate $\Gamma \sim G m^2 (\Delta x)^2 k_B T / \hbar$. The mathematical consistency of the framework is established through spectral analysis of the Laplace-Beltrami operator and the construction of exact solutions in constant curvature backgrounds.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18996069 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Complex Time and the Unification of Quantum, Thermal, and Geometric Degrees of Freedom A First-Principles Derivation li, yuanjian Complex Time Holomorphic Wavefunction Kähler Manifold Quantum Gravity Thermal Field Theory Liouville Equation Ryu–Takayanagi Formula Decoherence AdS/CFT <p>We present a first-principles derivation of a unified field theory that combines quantum dynamics, thermal field theory, and two-dimensional quantum gravity within a single holomorphic framework. The fundamental object is a complex time manifold $\mathcal{M}$---a compact Riemann surface with local coordinate $z = \tau/\ell_P + i t/\ell_P$, where $\ell_P$ is the Planck time. The quantum state is a holomorphic section $\Psi(z)$ of a line bundle over $\mathcal{M}$, and the geometry is encoded in a K\"ahler metric $ds^2 = \Omega^2(z,\bar{z})\,dz d\bar{z}$. Starting from the principle of least action, general covariance on $\mathcal{M}$, and the correspondence principle, we construct the total action $S = S_{\text{EH}} + S_{\text{matter}} + S_{\text{int}}$. Variation yields a coupled system: a modified wave equation for $\Psi$ that reduces to the Schr\"odinger equation in the flat limit, and a Liouville equation for $\Omega$ that encodes the feedback of quantum information on geometry. The KMS condition emerges as a natural boundary condition from the compactification of the imaginary time direction. We show that in the semi-classical limit, the theory reproduces the thermodynamics of black holes and predicts a fundamental decoherence mechanism with rate $\Gamma \sim G m^2 (\Delta x)^2 k_B T / \hbar$. The mathematical consistency of the framework is established through spectral analysis of the Laplace-Beltrami operator and the construction of exact solutions in constant curvature backgrounds.</p> |
| title | Complex Time and the Unification of Quantum, Thermal, and Geometric Degrees of Freedom A First-Principles Derivation |
| topic | Complex Time Holomorphic Wavefunction Kähler Manifold Quantum Gravity Thermal Field Theory Liouville Equation Ryu–Takayanagi Formula Decoherence AdS/CFT |
| url | https://doi.org/10.5281/zenodo.18996069 |