Complex Time and the Unification of Quantum, Thermal, and Geometric Degrees of Freedom A First-Principles Derivation

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Autor principal: li, yuanjian
Formato: Recurso digital
Lenguaje:inglés
Publicado: Zenodo 2026
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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>
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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