arXiv subjects

Jorge Meza-Domínguez

Publications and source records attributed to Jorge Meza-Domínguez.

7 recordsLinked to original sources

arXiv2026

Topological Quantization of Complex Velocity in Stochastic Spacetimes

We establish a formal geometric framework for quantum fields on a stochastic gravitational background. Starting from a master partition function that averages over metric fluctuations, we define a matter amplitude $\mathcal{K}[Φ; x]$ with explicit parametric dependence on spacetime coordinates, whose logarithmic derivative yields a complex velocity field $η_μ = π_μ - i u_μ$. This object is shown to be a section of the pullback bundle $E = π_2^*(T^*M)$ over the product of configuration space $\mathcal{C}$ and spacetime $M$, and defines a flat $\mathbb{C}^\times$ connection whose $U(1)$ part governs phase transport and whose $\mathbb{R}^+$ part governs scale transport. The coupled dynamics collapse into the complex geodesic equation $\mathcal{L}_ηη= d(|η|^2)$. On non-simply connected spacetimes, the total phase satisfies $\frac{m}{\hbar}\oint_γη_μ dx^μ = 2πn + Δϕ_{\mathrm{top}}$, demonstrated analytically for a scalar field with twisted boundary conditions on a conical spacetime. We provide a self-contained bundle isomorphism mapping $η_μ$ to the symmetric logarithmic derivative of quantum estimation theory, and derive the associated Berry curvature. A prospective estimate for the MAGIS-100 interferometer yields $γ_B \sim 3.97 \times 10^{-9}$ rad for an astrophysical stochastic background (approximately five orders below projected sensitivity) and $γ_B \sim 3.97 \times 10^{-53}$ rad for Planck-scale fluctuations. This framework geometrizes quantum mechanics without hidden variables: stochasticity imprints spacetime fluctuations on matter, preserving the wave function's probabilistic nature while maintaining consistency with the Born rule.

gr-qc↗

arXiv2026

Canonical Quantization and Constraint Algebra of Weyl-Invariant Gravity in a Conformal Gauge: Emergence of a Geometric Cosmological Term

We present the canonical quantization of Weyl-invariant gravity in a specific conformal gauge. Fixing the scale factor as $a(η) = 1/(H_0η)$ yields an effective geometric cosmological term $\mathcal{M}(η) = α/η^2$ on the left-hand side of the Einstein equations, guaranteeing an equation of state $w = -1$ by construction. The Bianchi identity requires a compensator scalar field; we show that this compensator is the conformal mode of the metric, a gauge artifact that does not propagate ghost instabilities in the full quantum theory. We develop the complete ADM Hamiltonian formulation and prove that the constraint algebra closes in standard first-class form. Canonical quantization yields a well-defined Wheeler-DeWitt equation where the $\mathcal{M}(η)$ term acts as a potential barrier dynamically suppressing the quantum creation of small-scale universes. The physical reduced Hamiltonian is demonstrated to be bounded from below, time evolution is strictly unitary in the physical Hilbert space, and microcausality is preserved. In the pure vacuum regime, the model admits an exact analytical solution with $Ω_{\text{DE}} = 1$, resolving the cosmic coincidence problem without fine-tuned parameters. In the matter-dominated era, the comoving horizon scales as $R_H \propto η$, so our result $\mathcal{M} \propto η^{-2} \propto R_H^{-2}$ reproduces the central Compton Mass Dark Energy (CMaDE) hypothesis from first principles and establishes $n = -2$ as the theoretical benchmark for the Conformal Holographic Dark Energy (CHDE) parametrization $\mathcal{M} \propto η^n$. From a pure conformal symmetry principle, the model delivers an effective geometric cosmological term that drives the accelerated expansion with $w = -1$, providing the missing action principle for CMaDE.

gr-qc↗

arXiv2026

Canonical Uncertainty Relations for Madelung Variables in Curved Spacetime: Relating Dark Matter Cores and Unruh Radiation

We establish fundamental uncertainty relations for the hydrodynamic variables arising from the Madelung representation of quantum fields in curved spacetime. Through canonical quantization of the density $n$ and phase $θ$ variables and their conjugate momenta, we derive exact uncertainty principles that depend on spacetime geometry through the lapse function $N$ and spatial metric $γ_{ij}$. These relations reveal how gravitational fields modulate quantum fluctuations and provide first-principles constraints for Scalar Field Dark Matter (SFDM) models and stochastic quantum gravity. We present two groundbreaking applications. First, By coupling the density-velocity uncertainty to the Newtonian condition of hydrostatic equilibrium, we derive the exact scaling law for the minimum core radius of a self-gravitating scalar field halo. We naturally find the scale $r_c \propto m^{-1/2}$ which is a testable prediction. Second, by evaluating the phase--momentum commutator in Rindler coordinates and relating the canonical momentum $Π_θ$ to the energy density via the Hamiltonian, we obtain the acceleration scale $k_B T = C\hbar a/c$. The proportionality constant $C=1/(2π)$ is fixed by the topological quantization of the Madelung phase circulation around the Euclidean horizon. This dual achievement demonstrates that quantum uncertainty on curved backgrounds is the unifying principle behind both galactic structure and black hole thermodynamics.

gr-qc↗

arXiv2026

Entanglement as a Witness of Quantum Coherence: A Bipartite Monty-Hall Protocol

We present a bipartite protocol inspired by the Monty Hall puzzle that operationally distinguishes quantum coherence from classical ignorance. A principal qutrit is entangled with an ancillary qutrit via a controlled unitary, preparing $|Ψ\rangle = \frac{1}{\sqrt{3}}(|A,0\rangle + |B,1\rangle + |C,2\rangle)$. A rank-1 projective discard then eliminates one basis state, leaving a coherent superposition of the two remaining states. Finally, the ancilla and qutrit are measured, yielding joint probabilities that encode the interplay between superposition and measurement back-action. We show that the conditional probability $P(B|\text{anc}=0)$ takes the value $1/4$ in both quantum mechanics and the classical ignorant-host model, making it unsuitable as a witness. The true quantum-classical separation emerges in conditional joint probabilities that correlate ancilla outcomes with specific discard operations. We define witnesses $\mathcal{W}_{i,j} = P(anc=i, qutrit=j \mid \text{discard } k)$ where $j$ differs from the ancilla-implied state. Quantum mechanics predicts $\mathcal{W} = 1/4$, while any classical epistemic model with perfect initial correlations yields $\mathcal{W} = 0$. We provide the explicit $9 \times 9$ unitary matrix, a complete analysis of all measurement outcomes, and a detailed proof of the violation. The witness is fully immune to white noise and robust against moderate dephasing. The protocol requires only a single pair of entangled qutrits and sequential measurements -- no spatial separation, no multiple copies, and no complex sets of incompatible observables. This makes it suitable for advanced undergraduate laboratories and provides a pedagogically accessible test of the ontic-epistemic distinction in quantum foundations.

quant-ph↗

arXiv2026

A Covariant Chiral-Hydrodynamic Formulation of the Dirac Equation in Curved Spacetime

The hydrodynamic formulation of the Dirac equation has historically been hindered by the inability to close the system of physical variables without resorting to infinite moment hierarchies. We resolve this longstanding issue by developing a fully covariant chiral-hydrodynamic formulation of the Dirac field in curved spacetime. Working in the Weyl representation, we introduce two independent null vectors, $P_L^μ$ and $P_R^μ$, which decouple the left and right chiral components. This allows us to define chiral geodesic and stochastic velocities, yielding a closed system of exactly eight real equations that corresponds directly to the Dirac field degrees of freedom. Remarkably, this formulation naturally isolates the spin-orbit coupling $(q/2)σ^{μν}F_{μν}$ while demonstrating the vanishing of the spin-gravity coupling in torsion-free general relativity. To demonstrate the analytical power of this framework, we specialize to the Schwarzschild geometry. We obtain exact radial solutions in terms of confluent Heun functions and directly compute the quasi-bound state spectrum (fermionic resonances), quasinormal mode frequencies, and greybody factors. Furthermore, by establishing an exact energy balance equation -- representing the first law of thermodynamics for Dirac fields -- we derive the Hawking radiation flux purely from chiral flux conservation at the event horizon. This work not only provides a closed hydrodynamic theory for spin-1/2 fluids but also establishes a unified framework for analyzing quantum information and fermion dynamics in strong gravitational backgrounds.

gr-qc↗

arXiv2026

Energy Balance of a Boson Gas at Zero Temperature in Curved Spacetime

We develop a comprehensive thermodynamic description for a zero-temperature boson gas in curved spacetime, integrating energy conservation with information-theoretic principles. Using the hydrodynamic Madelung representation within the ADM formalism, we establish two fundamental relationships: an energy balance equation representing the first law of thermodynamics from a spacetime perspective, and an information-theoretic constraint connecting Fisher entropy to the dynamical evolution of the boson density. This dual formulation clearly separates energy transport from information conservation while revealing how quantum information is preserved in curved backgrounds. The introduction of a stochastic velocity provides a bridge between quantum potential effects and underlying spacetime fluctuations. We demonstrate the consistency of our framework through detailed analyses of quantum systems in both Minkowski and Schwarzschild spacetimes. This work provides a unified foundation for studying relativistic bosonic systems, with direct relevance to boson stars and scalar field dark matter models.

gr-qc↗

arXiv2026

A Gauge-Invariant Bundle Isomorphism Between Complex Velocity Fields and Symmetric Logarithmic Derivatives

We establish a rigorous bundle isomorphism between the complex velocity field $η_μ = π_μ - i u_μ$, obtained by averaging matter dynamics over stochastic gravitational fluctuations, and the symmetric logarithmic derivative (SLD) operator $L_μ$ of quantum estimation theory. The isomorphism $\widetilde{\mathcal{T}}: Γ(E/{\sim}) \to Γ(\mathcal{L})$ maps gauge-equivalence classes of sections of the pullback bundle $E = π_2^*(T^*M)$ over $\mathcal{C} \times M$ to SLD operators on the Hilbert space $\mathcal{H}_0 = L^2(\mathcal{C}, ν_0)$, where $\mathcal{C}$ is the infinite-dimensional Fréchet manifold of matter fields and $ν_0$ is a fixed Gaussian measure. We prove that $\widetilde{\mathcal{T}}$ and the associated quantum Fisher metric are independent of the choice of $ν_0$, rendering the construction intrinsic to the physical probability density. The Fisher metric acquires a simple form in terms of the Madelung--Bohm velocities: $g_{μν}^{\mathrm{FS}} = \frac{4m^2}{\hbar^2} \bigl[\operatorname{Cov}(π_μ,π_ν) + \operatorname{Cov}(u_μ,u_ν)\bigr]_{\mathcal{P}}$. As a consequence, the flat $U(1)$ connection defined by $η_μ$ yields a quantized holonomy for non-contractible spacetime loops, predicting topological phases that may be observable in atom interferometry.

quant-ph↗