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

• URL: http://arxiv.org/abs/2604.21348v2
• Date: Mon, 27 Apr 2026 21:26:36 GMT
• Title: Ghost Degrees of Freedom Without Quantum Runaway: Exact Moment Bounds from an Operator Conservation Law
• Abstract summary: We prove a rigorous, state-independent upper bound on the mean squared phase-space radius for all time and every quantum state with initial second moments.<n>The interaction is bounded and vanishes at large separations, the generic situation in effective field theory.<n>The absence of confining potential means the proof is silent on spectral discreteness and the existence of a finite ground state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• From Qubit to Qubit: A Graduate Course in Quantum Mechanics [0.0]
  This textbook is drawn from notes for a two-semester graduate course in quantum mechanics.<n>The starting point is a single qubit, the smallest nontrivial space with the strongest possible restriction on its dynamics.
  arXiv  Detail & Related papers  (2026-05-02T19:16:40Z)
• Why Does Classical Turbulence Obey an Area Law? [0.0]
  In incompressible flow the viscous force is solenoidal, whereas the Made transform of a spinless Schrdinger equation produces only gradient forces.<n>Reducing the $N$-body density matrix to its one-body and closing the dynamics via Born-Markov yields Lindblad jump operators with $k2$ scattering rates.<n>Dissipation and forcing are not separate ingredients: both come from the same Lindblad operators, and their amplitudes are locked by the QSD structure.
  arXiv  Detail & Related papers  (2026-04-21T07:38:15Z)
• Time Symmetry, Retrocausality, and Emergent Collapse: The Tlalpan Interpretation of Quantum Mechanics [51.56484100374058]
  The Tlalpan Interpretation (QTI) proposes that the wavefunction collapse is not a primitive, axiomatic rule but an emergent phenomenon.<n>The novelty of QTI lies in its embedding of collapse within the conceptual language of critical phenomena in statistical physics.
  arXiv  Detail & Related papers  (2025-08-25T20:30:56Z)
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators [50.24983453990065]
  This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles.<n>We derive in the weak coupling limit the reservoir statistics, which is determined by whose terms in the multi-point correlation functions of the reservoir are non-zero in the WCL.<n>We prove that the resulting reduced system dynamics converges to unitary dynamics with a modified Hamiltonian which can be interpreted as a Lamb shift to the original Hamiltonian.
  arXiv  Detail & Related papers  (2025-05-13T05:32:34Z)
• Universal bound on the relaxation rates for quantum Markovian dynamics [0.0]
  We show that a maximal rate is bounded from above by the sum of all the relaxation rates divided by the dimension of the Hilbert space. This constraint is universal (it is valid for all quantum systems with finite number of energy levels) and it is tight (cannot be improved)
  arXiv  Detail & Related papers  (2024-08-31T12:15:45Z)
• A non-hermitean momentum operator for the particle in a box [49.1574468325115]
  We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example. The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
  arXiv  Detail & Related papers  (2024-03-20T12:51:58Z)
• Quantizing the Quantum Uncertainty [0.0]
  We discuss the quantization of the quantum uncertainty as an operator acting on wave-functions over field space. We show how this spectrum appears in the value of the coupling of the effective conformal potential driving the evolution of extended Gaussian wave-packets. We conclude with an open question: is it possible to see experimental signatures of the quantization of the quantum uncertainty in non-relativistic physics?
  arXiv  Detail & Related papers  (2023-07-03T14:40:14Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Quantum Physics from Number Theory [0.0]
  Quantum properties are derived from number theoretic attributes of trigonometric functions applied to an explicitly ensemble-based representation of Hilbert states. Quantum mechanics is itself a singular limit of this number-theoretic model at $p=infty$.
  arXiv  Detail & Related papers  (2022-09-12T19:04:14Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)
• Universal Error Bound for Constrained Quantum Dynamics [0.0]
  We establish an observable-based error bound for a constrained-dynamics approximation in generic gapped quantum systems. Our work establishes a universal and rigorous result concerning nonequilibrium quantum dynamics.
  arXiv  Detail & Related papers  (2020-01-03T06:25:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.