Euclidean quantum mechanics and stochastic processes

Preface / Forward / Acknowledgements / Introduction / Invitation to Stochastic Calculus / Hydrodynamical Formulation of Quantum Mechanics / Stochastic Diffusion Processes / Selected Problems in Stochastic Mechanics / Stochastic Variational Principles / Euclidean Quantum Mechanics / Stochastic Path Space Picture / Relativistic Stochastic Mechanics / Dirac Equation - Stochastic Viewpoint / Stochastic Field Theory / Stochastic Mechanics on Manifolds / Stochastic Route to Quantum Mechanics - Quest Continues / References / Author Index / Subject Index.Preface / Forward / Acknowledgements / Introduction / Invitation to Stochastic Calculus / Hydrodynamical Formulation of Quantum Mechanics / Stochastic Diffusion Processes / Selected Problems in Stochastic Mechanics / Stochastic Variational Principles / Euclidean Quantum Mechanics / Stochastic Path Space Picture / Relativistic Stochastic Mechanics / Dirac Equation - Stochastic Viewpoint / Stochastic Field Theory / Stochastic Mechanics on Manifolds / Stochastic Route to Quantum Mechanics - Quest Continues / References / Author Index / Subject Index.

Jan 1, 20084 citations

Rotational Inertia under Euclidean Variation

Wang Kianming

We propose a mathematical mechanism for quantum fluctuations based on Euclidean self-return. A complex metric path connects Lorentzian and Euclidean sections without becoming degenerate. A Euclidean return potential and positive configuration-space inertia generate repeated metric-phase motion. After projection and mixing, this motion defines a centered process with finite Green–Kubo action $\mathcal A_*$ . Under a causal, unit-gain response assumption, a particle of mass $m$ acquires the diffusion coefficient $D_{\mathrm q}(m)=\frac{\mathcal A_*}{2m}$ Within time-symmetric stochastic mechanics, the same action scale produces the Bohm quantum-potential form and the fluctuation bound $\Delta x\,\Delta p_{\mathrm{fl}}\geq\frac{\mathcal A_*}{2}$ These results motivate the conjecture $\mathcal A_*=\hbar$ . The proposed mechanism is conditional on the stated mixing and response assumptions and does not treat microscopic white noise as fundamental. **Keywords** Euclidean variation; rotational inertia; complex metrics; quantum fluctuations; stochastic mechanics; Green–Kubo relation; quantum potential; Planck constant.We propose a mathematical mechanism for quantum fluctuations based on Euclidean self-return. A complex metric path connects Lorentzian and Euclidean sections without becoming degenerate. A Euclidean return potential and positive configuration-space inertia generate repeated metric-phase motion. After projection and mixing, this motion defines a centered process with finite Green–Kubo action $\mathcal A_*$. Under a causal, unit-gain response assumption, a particle of mass $m$ acquires the diffusion coefficient $$D_{\mathrm q}(m)=\frac{\mathcal A_*}{2m}$$ Within time-symmetric stochastic mechanics, the same action scale produces the Bohm quantum-potential form and the fluctuation bound $$\Delta x\,\Delta p_{\mathrm{fl}}\geq\frac{\mathcal A_*}{2}$$ These results motivate the conjecture $\mathcal A_*=\hbar$. The proposed mechanism is conditional on the stated mixing and response assumptions and does not treat microscopic white noise as fundamental. **Keywords** Euclidean variation; rotational inertia; complex metrics; quantum fluctuations; stochastic mechanics; Green–Kubo relation; quantum potential; Planck constant.

Aug 29, 20260 citations

STOCHASTIC PROCESSES AND QUANTUM MECHANICS

Giovanni Jona-Lasinio

AstérisqueJan 1, 19835 citations

\mathcal A_*

. Under a causal, unit-gain response assumption, a particle of mass

m

acquires the diffusion coefficient

D_{\mathrm q}(m)=\frac{\mathcal A_*}{2m}

Within time-symmetric stochastic mechanics, the same action scale produces the Bohm quantum-potential form and the fluctuation bound

\Delta x\,\Delta p_{\mathrm{fl}}\geq\frac{\mathcal A_*}{2}

These results motivate the conjecture

\mathcal A_*=\hbar

. The proposed mechanism is conditional on the stated mixing and response assumptions and does not treat microscopic white noise as fundamental. **Keywords** Euclidean variation; rotational inertia; complex metrics; quantum fluctuations; stochastic mechanics; Green–Kubo relation; quantum potential; Planck constant.