Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part I: Generalizing the Liouville Equation
- URL: http://arxiv.org/abs/2603.20399v1
- Date: Fri, 20 Mar 2026 18:19:21 GMT
- Title: Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part I: Generalizing the Liouville Equation
- Abstract summary: We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant generalization of Hamiltonian dynamics.<n>The question to what extent this equation can be interpreted in terms of objective field theories is discussed in a companion paper.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign sharp values to all observables and thereby avoid the quantum measurement problem. In classical mechanics, motion is deterministic and corresponds to an evolution of the phase space probability density according to Liouville's equation that is governed by first derivatives of the Hamiltonian in phase space. We derive a generalization of the Liouville equation with natural constraints -- namely, reduction to classical Hamiltonian dynamics as the stochasticity parameter $\hbar\mapsto0$, Fokker-Planck form for the probability density evolution, local Hamiltonian dependence, time-reversal invariance, energy conservation, and minimality -- which turns out to be a Fokker-Planck equation with a generalized diffusion matrix that is symmetric, traceless, and constructed from the Hessian of the Hamiltonian. We then show that the Schrödinger equation in the coherent-state phase-space formulation of certain bosonic QFTs has precisely this form, with the Husimi function playing the role of the phase space probability density. The question to what extent this equation can be interpreted in terms of objective stochastic field theories is discussed in a companion paper.
Related papers
- Quantum simulation of the Liouville equation in classical mechanics with discontinuous potential via Schrödingerization [42.22857110018992]
We develop quantum simulation algorithms for the Liouville equation of classical mechanics with discontinuous potential.<n>We combine Hamiltonian-preserving schemes by Jin and Wen in Commun. Math. Sci. 3(3), 285-315 (2005) with the Schrdingerization method, which embeds the resulting nonunitary semi-discrete dynamics into a unitary Schrdinger type system.
arXiv Detail & Related papers (2026-06-13T02:49:05Z) - Quantum optomechanics of lossy bodies: general approach and structured squeezed vacuum effects [51.56484100374058]
We investigate the overall optomechanical force experienced by a macroscopic lossy object in free space under external quantum illumination.<n>By driving the scattering field with an anisotropic, multimode squeezed vacuum state, the spatial profile of the electromagnetic quantum fluctuations can be engineered to exhibit broken rotational symmetry.<n>We establish a general formalism for macroscopic quantum optomechanics that operates beyond the constraints of thermal equilibrium.
arXiv Detail & Related papers (2026-04-07T13:25:43Z) - Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part II: Prospects for a Trajectory Interpretation [0.0]
We show that every $Q$-function can be represented as a weighted average of conditional probabilities over boundary values.<n>Despite this limitation, we show that Drummond's trajectory dynamics are fundamentally non-Markovian.
arXiv Detail & Related papers (2026-03-30T20:31:35Z) - Toda-like Hamiltonian as a probe for quantized prey-predator dynamics [0.0]
Phase-space features of a reduced version of the Toda-like Hamiltonian, $mathcalH(x,,k)$, written in a form constrained by the condition $partial2 mathcalH / partial x partial k = 0$, are analyzed.<n>The exact profile of the quantum distortions over classical prey-predator phase-space trajectories is obtained non-perturbatively.
arXiv Detail & Related papers (2026-03-10T01:29:17Z) - Derivation of Fokker-Planck equation from Schrodinger dynamics [0.0]
We derive the Fokker_Planck equation through a purely quantum mechanical approach based on the reversible Schrodinger dynamics.<n>Because of the use of the representation of eigenstates of the time-independent Hamiltonian in our derivation, the thermodynamical entropy in this case must correspond to a coarse-graining of the quantum entropy.
arXiv Detail & Related papers (2025-05-28T11:51:30Z) - Quantum mechanics without quantum potentials [0.0]
Non-locality in quantum mechanics can be resolved by considering relativistically covariant diffusion in spacetime.
We introduce the concept of momentum equilinear to replace the second-order Bohm-Newton equations of motion.
arXiv Detail & Related papers (2024-01-08T18:51:38Z) - Real-time dynamics of false vacuum decay [49.1574468325115]
We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential.
We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
arXiv Detail & Related papers (2023-10-06T12:44:48Z) - 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) - Correspondence Between the Energy Equipartition Theorem in Classical
Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
In quantum mechanics, the energy per degree of freedom is not equally distributed.
We show that in the high-temperature regime, the classical result is recovered.
arXiv Detail & Related papers (2022-05-24T20:51:03Z) - Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
Quantization smears the gravitational singularity avoiding its localization in the configuration space.
Results suggest that the generic singularity of general relativity can be avoided at quantum level.
arXiv Detail & Related papers (2022-04-24T13:32:45Z) - Probabilistic deconstruction of a theory of gravity, Part I: flat space [0.0]
We show that Einstein's equations of the theory arise in the semi-classical limit of the quantum evolution of probability under the process.
In particular, in flat Jackiw-Teitelboim gravity, the area of compactified space solved for by Einstein's equations can be identified as a probability density evolving under the Markovian process.
arXiv Detail & Related papers (2021-08-24T18:52:31Z)
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.