General-relativistic wave$-$particle duality with torsion

• URL: http://arxiv.org/abs/2211.03234v3
• Date: Thu, 4 Jul 2024 17:42:22 GMT
• Title: General-relativistic wave$-$particle duality with torsion
• Authors: Francisco Ribeiro Benard Guedes, Nikodem Janusz Popławski,
• Abstract summary: We show that the four-velocity of a Dirac particle is related to its relativistic wave function by $ui=barpsigammaipsi/barpsipsi$. This relativistic wave$-$particle duality relation is demonstrated for a free particle related to a plane wave in a flat spacetime.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose that the four-velocity of a Dirac particle is related to its relativistic wave function by $u^i=\bar{\psi}\gamma^i\psi/\bar{\psi}\psi$. This relativistic wave$-$particle duality relation is demonstrated for a free particle related to a plane wave in a flat spacetime. For a curved spacetime with torsion, the momentum four-vector of a spinor is related to a generator of translation, given by a covariant derivative. The spin angular momentum four-tensor of a spinor is related to a generator of rotation in the Lorentz group. We use the covariant conservation laws for the spin and energy$-$momentum tensors for a spinor field in the presence of the Einstein$-$Cartan torsion to show that if the wave satisfies the curved Dirac equation, then the four-velocity, four-momentum, and spin satisfy the classical Mathisson$-$Papapetrou equations of motion. We show that these equations reduce to the geodesic equation. Consequently, the motion of a particle guided by the four-velocity in the pilot-wave quantum mechanics coincides with the geodesic motion determined by spacetime. We also show how the duality and the operator form of the Mathisson$-$Papapetrou equations arise from the covariant Heisenberg equation of motion in the presence of torsion.

Related papers

• Biquaternion representation of the spin one half and its application on the relativistic one electron atom [65.268245109828]
  In this work we represent the $1/2$ Spin particles with complex quaternions. We determine the states, rotation operators and the total angular momentum function in the complex quaternion space.
  arXiv  Detail & Related papers  (2024-02-28T19:24:13Z)
• Double-scale theory [77.34726150561087]
  We present a new interpretation of quantum mechanics, called the double-scale theory. It is based on the simultaneous existence of two wave functions in the laboratory reference frame. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
  arXiv  Detail & Related papers  (2023-05-29T14:28:31Z)
• Coherent transfer of the transverse momentum of an optical vortex beam to the motion of a single trapped ion [22.42090005507693]
  We demonstrate the excitation, using a structured light beam carrying orbital angular momentum, of the center of mass motion of a single atom. We characterize the coherent interaction by an effective transverse Lamb-Dicke factor $etamathrmexp_perp62(5)$ which is in agreement with our theoretical prediction $etamathrmtheo_perp57(1)$
  arXiv  Detail & Related papers  (2022-06-10T06:15:08Z)
• Asymmetric particle-antiparticle Dirac equation: first quantization [0.0]
  We derive a Dirac-like equation, the asymmetric Dirac equation, where particles and antiparticles sharing the same wave number have different energies and momenta. We obtain a formal connection between the asymmetric Dirac equation and the standard Dirac equation. We show that by properly adjusting the free parameters of the present wave equation we can make it reproduce the predictions of the usual Dirac equation.
  arXiv  Detail & Related papers  (2022-05-09T18:36:37Z)
• Relativistic Mechanics Theory for Electrons that Exhibits Spin, Zitterbewegung, Superposition and Produces Dirac's Wave Equation [0.0]
  The spin of an electron is a natural part of its space-time path as a point particle. The total motion can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called the spin center.
  arXiv  Detail & Related papers  (2021-08-14T02:45:03Z)
• Comment on `Relativistic wave-particle duality for spinors' [0.0]
  We point out that, in line with existing literature on Einstein-Cartan gravity with torsion, the spin-torsion term should represent negative energy. We suggest a possible resolution of that dilemma.
  arXiv  Detail & Related papers  (2021-03-07T22:09:55Z)
• Relativistic wave--particle duality for spinors [0.0]
  relativistic wave--particle duality can be embodied in a relation $langle uirangle=barpsigammaipsi/barpsipsi$. We use the Einstein-Cartan theory of gravity with torsion, which incorporates the spin-orbit interaction in curved spacetime.
  arXiv  Detail & Related papers  (2021-01-11T22:06:27Z)
• Gravitational decoherence: a non relativistic spin 1/2 fermionic model [0.0]
  We derive a non relativistic model for the gravitational decoherence of spin 1/2 particles. We discuss the differences with the scalar bosonic model and we describe the regimes in which they become negligible.
  arXiv  Detail & Related papers  (2020-12-02T16:54:00Z)
• Zitterbewegung of massless particles [91.3755431537592]
  Zitterbewegung of massless particles with an arbitrary spin is analyzed in various representations. Zitterbewegung takes place in any representation except for the Foldy-Wouthuysen one.
  arXiv  Detail & Related papers  (2020-08-12T14:16:44Z)
• Position and spin in relativistic quantum mechanics [68.8204255655161]
  The position and spin operators in the Foldy-Wouthuysen representation are quantum-mechanical counterparts of the classical position and spin variables. The spin-orbit interaction does not exist for a free particle if the conventional operators of the orbital angular momentum and the rest-frame spin are used.
  arXiv  Detail & Related papers  (2020-03-14T07:49:40Z)
• Zitterbewegung and Klein-tunneling phenomena for transient quantum waves [77.34726150561087]
  We show that the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime.
  arXiv  Detail & Related papers  (2020-03-09T21:27:02Z)

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.