A Bundle Isomorphism Relating Complex Velocity to Quantum Fisher Operators

• URL: http://arxiv.org/abs/2604.12187v2
• Date: Thu, 16 Apr 2026 14:28:17 GMT
• Title: A Bundle Isomorphism Relating Complex Velocity to Quantum Fisher Operators
• Abstract summary: We show that averaging matter dynamics over gravitational fluctuations gives rise to a complex velocity field (_ = _ - i u_) living as a section of the pullback bundle (E = _2*(T*M)to mathcalCtimes M.<n>We prove that (_) is isomorphic, via the Schrdinger representation, to the symmetric logarithmic derivative (SLD) operator (L_) on the Hilbert space (mathcalH
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that averaging matter dynamics over stochastic gravitational fluctuations gives rise to a complex velocity field \(η_μ = π_μ - i u_μ\) living as a section of the pullback bundle \(E = π_{2}^{*}(T^{*}M)\to \mathcal{C}\times M\). We prove that \(η_μ\) is isomorphic, via the Schrödinger representation, to the symmetric logarithmic derivative (SLD) operator \(L_μ\) on the Hilbert space \(\mathcal{H}_{x} = L^{2}(\mathcal{C})\), up to a trace-zero projection. This isomorphism \(\widetilde{\mathcal{T}}:Γ(E / \sim)\to Γ(\mathcal{L})\) is a bundle isomorphism preserving the flat \(U(1)\) connection (proved in \cite{meza2026topological}) and the quantum Fisher metric. The quantum Fisher information metric \(g_{μν}^{\mathrm{FS}}\) is expressed directly in terms of \(η_μ\) as \(g_{μν}^{\mathrm{FS}} = - \frac{4m^{2}}{\hbar^{2}}\mathrm{Re}\langle (η_μ - \langle η_μ\rangle)(η_ν - \langle η_ν\rangle)\rangle_{\mathcal{P}}\). The holonomy of \(η_μ\) is quantized, leading to topological phases observable in atom interferometry.

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