Ghost Degrees of Freedom Without Quantum Runaway: Exact Moment Bounds from an Operator Conservation Law

Quantum Physics [Submitted on 23 Apr 2026] Ghost Degrees of Freedom Without Quantum Runaway: Exact Moment Bounds from an Operator Conservation Law Christopher Ewasiuk, Stefano Profumo We prove an exact quantum conservation law for a harmonic oscillator coupled to a ghost degree of freedom: a second classical conserved quantity lifts to a quantum operator that commutes with the Hamiltonian with no hbar corrections, yielding a rigorous, state-independent upper bound on the mean squared phase-space radius for all time and every quantum state with finite initial second moments. The proof uses only canonical commutation relations and the Leibniz rule; it requires no confining potential, no spectral assumptions, and no perturbative expansion. The interaction studied here is bounded and vanishes at large separations, the generic situation in effective field theory, yet this suffices to guarantee quantum stability in the sense of bounded second moments. Three independent numerical frameworks (Heisenberg picture, Schrodinger picture, and Fock-space diagonalization) confirm wavepacket confinement below the analytic bound, a real energy spectrum, and Poisson level statistics numerically consistent with an integrable structure. The absence of a confining potential means the proof is silent on spectral discreteness and the existence of a ground state; those questions, addressed for polynomial confining interactions in concurrent work, remain open for the interaction class studied here and represent the sharpest targets for future work. Ghost quantum instability is therefore not an inevitable consequence of a wrong-sign kinetic term but depends critically on the interaction structure. Comments: 11 pages, 4 figures Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2604.21348 [quant-ph]   (or arXiv:2604.21348v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.21348 Focus to learn more Submission history From: Christopher Ewasiuk [view email] [v1] Thu, 23 Apr 2026 07:06:58 UTC (1,021 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: hep-th References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)