Geometric post-Newtonian description of massive spin-half particles in curved spacetime

• URL: http://arxiv.org/abs/2307.04743v3
• Date: Sun, 29 Oct 2023 12:49:36 GMT
• Title: Geometric post-Newtonian description of massive spin-half particles in curved spacetime
• Authors: Ashkan Alibabaei, Philip K. Schwartz, Domenico Giulini
• Abstract summary: We consider the Dirac equation coupled to an external electromagnetic field in curved four-dimensional spacetime with a given timelike worldline $gamma$ representing a classical clock. We use generalised Fermi normal coordinates in a tubular neighbourhood of $gamma$ and expand the Dirac equation up to, and including, the second order in the dimensionless parameter. We give the weak-gravity post-Newtonian expression for the Pauli Hamiltonian of a spin-half particle in an external electromagnetic field.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the Dirac equation coupled to an external electromagnetic field in curved four-dimensional spacetime with a given timelike worldline $\gamma$ representing a classical clock. We use generalised Fermi normal coordinates in a tubular neighbourhood of $\gamma$ and expand the Dirac equation up to, and including, the second order in the dimensionless parameter given by the ratio of the geodesic distance to the radii defined by spacetime curvature, linear acceleration of $\gamma$, and angular velocity of rotation of the employed spatial reference frame along $\gamma$. With respect to the time measured by the clock $\gamma$, we compute the Dirac Hamiltonian to that order. On top of this `weak-gravity' expansion we then perform a post-Newtonian expansion up to, and including, the second order of $1/c$, corresponding to a `slow-velocity' expansion with respect to $\gamma$. As a result of these combined expansions we give the weak-gravity post-Newtonian expression for the Pauli Hamiltonian of a spin-half particle in an external electromagnetic field. This extends and partially corrects recent results from the literature, which we discuss and compare in some detail.

Related papers

• Additional dimensions of space and time in the domain of deep inelastic processes [0.0]
  We derive a formula for estimating the speed $U*$ of a virtual particle in indirect measurements. The new angular parameters are closely related to the type of the phase-space geometry and dimensionality of the space-time continuum.
  arXiv  Detail & Related papers  (2024-08-04T09:57:15Z)
• Relativistic and nonrelativistic Landau levels for Dirac fermions in the cosmic string spacetime in the context of rainbow gravity [0.0]
  We study the relativistic and nonrelativistic Landau levels for Dirac fermions in the cosmic string spacetime. We graphically analyze the behavior of Landau levels for the three rainbow gravity scenarios.
  arXiv  Detail & Related papers  (2024-03-03T01:48:15Z)
• Vacuum Force and Confinement [65.268245109828]
  We show that confinement of quarks and gluons can be explained by their interaction with the vacuum Abelian gauge field $A_sfvac$.
  arXiv  Detail & Related papers  (2024-02-09T13:42:34Z)
• Ultracold Neutrons in the Low Curvature Limit: Remarks on the post-Newtonian effects [49.1574468325115]
  We apply a perturbative scheme to derive the non-relativistic Schr"odinger equation in curved spacetime. We calculate the next-to-leading order corrections to the neutron's energy spectrum. While the current precision for observations of ultracold neutrons may not yet enable to probe them, they could still be relevant in the future or in alternative circumstances.
  arXiv  Detail & Related papers  (2023-12-30T16:45:56Z)
• Universal role of curvature in vacuum entanglement [0.0]
  We highlight some universal features concerning the role of spacetime curvature in the entanglement induced between quantum probes coupled to a quantum field in a suitable vacuum state. Our analysis shows that curvature can induce entanglement features in certain regions of the above parameter space, in a manner which facilitates using entanglement as a probe of spacetime curvature.
  arXiv  Detail & Related papers  (2023-11-25T13:14:33Z)
• General-relativistic wave$-$particle duality with torsion [0.0]
  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.
  arXiv  Detail & Related papers  (2022-11-06T23:09:57Z)
• A New Look at the $C^{0}$-formulation of the Strong Cosmic Censorship Conjecture [68.8204255655161]
  We argue that for generic black hole parameters as initial conditions for Einstein equations, the metric is $C0$-extendable to a larger Lorentzian manifold. We prove it violates the "complexity=volume" conjecture for a low-temperature hyperbolic AdS$_d+1$ black hole dual to a CFT living on a ($d-1$)-dimensional hyperboloid $H_d-1$.
  arXiv  Detail & Related papers  (2022-06-17T12:14:33Z)
• 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)
• Remarks on Fermions in a Dipole Magnetic Field [0.0]
  This work is a continuation of our recent study of non-relativistic charged particles, confined to a sphere enclosing a magnetic dipole at its center. We extend our computations in two significant ways. The first is to a relativistic spin-$frac12$ fermion and the second concerns the interpretation of the physics.
  arXiv  Detail & Related papers  (2021-07-21T13:42:03Z)
• 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)
• The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations. This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry. We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
  arXiv  Detail & Related papers  (2020-11-12T06:57:10Z)

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.