From Mass-Shell Factorisation to Spin: An Attempt at a Matrix-Valued Liouville Framework for Relativistic Classical and Quantum Phase-Spacetime

• URL: http://arxiv.org/abs/2505.03551v4
• Date: Tue, 03 Jun 2025 13:24:59 GMT
• Title: From Mass-Shell Factorisation to Spin: An Attempt at a Matrix-Valued Liouville Framework for Relativistic Classical and Quantum Phase-Spacetime
• Abstract summary: While Liouville's theorem is first-order in time for the phase-space distribution itself, the relativistic mass-shell constraint $pmu p_mu = m2$ is naively second-order in energy.<n>We argue that it is reasonable to unify both energy branches within a single Hamiltonian by factorizing $(p2 - m2)$ in analogy with Dirac's approach in relativistic quantum mechanics.<n>We show the resulting matrix-based Liouville equation remains first order and naturally yields a $4times4$ matrix-valued probability density function in phase
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: While Liouville's theorem is first-order in time for the phase-space distribution itself, the relativistic mass-shell constraint $p^\mu p_\mu = m^2$ is naively second-order in energy. We argue that it is reasonable to unify both energy branches within a single Hamiltonian by factorizing $(p^2 - m^2)$ in analogy with Dirac's approach in relativistic quantum mechanics. We show the resulting matrix-based Liouville equation remains first order and naturally yields a $4\times4$ matrix-valued probability density function in phase space as a classical analogue of a relativistic spin-half Wigner function. We investigate its classical physics and deformation quantisation.

Related papers

• Spinor Structure from Relativistic Mass-Shell Factorisation in Phase Space [0.0]
  We show that an overly restrictive Hamiltonian structure on relativistic phase space can give a non-quantum origin for spinor structure.<n>Results suggest a non-quantum origin for spinor structure and a route to reconciling relativistic covariance, classical phase-space transport, and quantum spin.
  arXiv  Detail & Related papers  (2026-08-29T16:18:27Z)
• Transmutation based Quantum Simulation for Non-unitary Dynamics [35.35971148847751]
  We present a quantum algorithm for simulating dissipative diffusion dynamics generated by positive semidefinite operators of the form $A=Ldagger L$.<n>Our main tool is the Kannai transform, which represents the diffusion semigroup $e-TA$ as a Gaussian-weighted superposition of unitary wave propagators.
  arXiv  Detail & Related papers  (2026-01-07T05:47:22Z)
• Quantum, Stochastic, and Classical Dynamics Within A Single Geometric Framework [0.0]
  We show that the Koopman--von Neumann (KvN) phase of classical mechanics emerges naturally as the $lambda to 1$ limit of this $sigma$--$lambda$ hierarchy.<n>This unified picture links quantum, and classical dynamics within a single continuous framework.
  arXiv  Detail & Related papers  (2025-10-31T04:46:39Z)
• Classical Representation for Quantum States of a Particle in $λ z^{2m}$ potential [0.0]
  A classical representation for quantum eigenstates of a particle bound in $lambda z2m$ $(lambda >0, m=1,2,...)$ potentials is developed.<n>The corresponding Schr"odinger equation in classical representation is analyzed.
  arXiv  Detail & Related papers  (2025-10-21T17:04:31Z)
• Quantum state discrimination in a $\mathcal{PT}$-symmetric system of a single trapped ion [6.852781781113404]
  We experimentally demonstrate an quantum state discrimination of two qubit states under a non-Hermitian Hamiltonian with parity-time-reversal symmetry.<n>Our work shows a promising application of non-Hermitian physics in quantum information processing.
  arXiv  Detail & Related papers  (2025-02-28T05:04:24Z)
• Producing Energy Eigenstates of the ${\rm H}_{2}$ Molecule by Classically Emulated Quantum Simulation [0.0]
  We produce an energy eigenstate of the $rm H_2$ molecule from a superposition of energy eigenstates by classically emulated quantum simulation.<n>We use a Hamiltonian of the $rm H_2$ molecule represented by Pauli matrices and ancillad qubits.
  arXiv  Detail & Related papers  (2024-12-30T02:52:01Z)
• Spin dynamics and dark particle in a weak-coupled quantum Ising ladder with $\mathcal{D}_8^{(1)}$ spectrum [7.16653440475268]
  Emergent Ising$_h2$ integrability is anticipated in a quantum Ising ladder composed of two weakly coupled, critical transverse field Ising chains. We show that the selection rule to the form factor, which is inherent in the intrinsic charge-parity $mathcalC$ of the Ising$_h2$ particles, causes a significant result. The long lifetime of dark particle suggests its potential as a stable qubit for advancing quantum information technology.
  arXiv  Detail & Related papers  (2024-02-17T09:12:59Z)
• 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)
• A Regularized $(XP)^2$ Model [0.5729101515196013]
  We investigate a dynamic model described by the classical Hamiltonian $H(x,p)=(x2+a2)(p2+a2)$, where $a2>0$, in classical, semi-classical, and quantum mechanics. We present three different forms of quantized Hamiltonians, and reformulate them into the standard Schr" odinger equation with $cosh 2x$-like potentials.
  arXiv  Detail & Related papers  (2023-08-18T01:34:57Z)
• Quantum propagator for a general time-dependent quadratic Hamiltonian: Application to interacting oscillators in external fields [0.0]
  We find the quantum propagator for a general time-dependent quadratic Hamiltonian. The state and excitation propagation along the harmonic chain in the absence and presence of an external classical source is studied and discussed.
  arXiv  Detail & Related papers  (2023-05-30T14:17:04Z)
• Relations between quantum metrology and criticality in general su(1, 1) systems [10.335953738568353]
  We show that the determination of the generator in the parameterization can be treated as an extended brachistochrone problem. By investigating the dynamic sensing proposals of three quantum critical systems, we show that the behavior of sensitivity is consistent with our predictions.
  arXiv  Detail & Related papers  (2023-03-19T13:39:32Z)
• Studying chirality imbalance with quantum algorithms [62.997667081978825]
  We employ the (1+1) dimensional Nambu-Jona-Lasinio (NJL) model to study the chiral phase structure and chirality charge density of strongly interacting matter. By performing the Quantum imaginary time evolution (QITE) algorithm, we simulate the (1+1) dimensional NJL model on the lattice at various temperature $T$ and chemical potentials $mu$, $mu_5$.
  arXiv  Detail & Related papers  (2022-10-06T17:12:33Z)
• 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)
• Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality [69.62715388742298]
  We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs) We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT.
  arXiv  Detail & Related papers  (2022-03-08T14:47:39Z)
• Relativistic quantum field theory of stochastic dynamics in the Hilbert space [8.25487382053784]
  We develop an action formulation of dynamics in the Hilbert space. By coupling the random to quantum fields, we obtain a random-number action which has the statistical spacetime translation. We prove that the QFT is renormal even in the presence of interaction.
  arXiv  Detail & Related papers  (2021-12-28T04:58:43Z)
• Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans\"atze [13.651587339535961]
  We develop a framework for convolutional quantum circuits with SU$(d)$symmetry. We prove Harrow's statement on equivalence between $nameSU(d)$ and $S_n$ irrep bases.
  arXiv  Detail & Related papers  (2021-12-14T18:03:43Z)
• Non-zero momentum requires long-range entanglement [6.018940870331878]
  We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum. The statement can also be generalized to fermion systems.
  arXiv  Detail & Related papers  (2021-12-13T19:00:04Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Probing quantum effects with classical stochastic analogs [0.0]
  We propose a method to construct a classical analog of an open quantum system. The classical analog is made out of a collection of identical wells where classical particles of mass $m$ are trapped.
  arXiv  Detail & Related papers  (2020-12-13T18:02:27Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)
• Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
  Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. Operators of the form $hatcal H=hatA+ihatB$ are described. Rigorous analytical analysis is performed for both wave and Green's functions.
  arXiv  Detail & Related papers  (2020-10-13T15:50:49Z)
• Quantum and classical approaches in statistical physics: some basic inequalities [0.0]
  We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. We derive the semiclassical limits for four cases, that is, for $hbarto0$, $Ttoinfty$, $omegato0$, and $Ntoinfty$.
  arXiv  Detail & Related papers  (2020-06-19T19:06:10Z)
• Work statistics in the periodically driven quartic oscillator: classical versus quantum dynamics [0.0]
  We study an anharmonic oscillator driven by a periodic external force with slowly varying amplitude both classically and within the framework of quantum mechanics. For both classical and quantum case we provide an intuitive explanation for the periodic variation of $P(E_f|E_i)$ with the maximal amplitude.
  arXiv  Detail & Related papers  (2020-04-22T10:31:29Z)

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.