Dirac Equation with Space Contributions Embedded in a Quantum-Corrected Gravitational Field

• URL: http://arxiv.org/abs/2408.10598v2
• Date: Mon, 11 Nov 2024 09:32:11 GMT
• Title: Dirac Equation with Space Contributions Embedded in a Quantum-Corrected Gravitational Field
• Authors: M. Baradaran, L. M. Nieto, S. Zarrinkamar,
• Abstract summary: The Dirac equation is considered with the recently proposed generalized gravitational interaction (Kepler or Coulomb) The general idea in choosing the metric is that the spacetime contributions are contained in an external potential or in an electromagnetic potential. The impossibility of solving our equation for the quantum-corrected Coulomb terms using known exact or quasi-exact nonperturbative analytical techniques is discussed.
• Score: 0.0
• License:
• Abstract: The Dirac equation is considered with the recently proposed generalized gravitational interaction (Kepler or Coulomb), which includes post-Newtonian (relativistic) and quantum corrections to the classical potential. The general idea in choosing the metric is that the spacetime contributions are contained in an external potential or in an electromagnetic potential which can be considered as a good basis for future studies of quantum physics in space. The forms considered for the scalar potential and the so-called vector (magnetic) potential, can be viewed as the multipole expansion of these terms and therefore the approach includes a simultaneous study of multipole expansions to both fields. We also discuss several known generalizations of the Coulomb potential within this formulation in terms of certain Heun functions. The impossibility of solving our equation for the quantum-corrected Coulomb terms using known exact or quasi-exact nonperturbative analytical techniques is discussed, and finally the Bethe-ansatz approach is proposed to overcome this challenging problem.

Related papers

• Dirac Equation Solution with Generalized tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra [0.0]
  We use a generalized tanh shaped hyperbolic potential to investigate bound state solutions of the Dirac equation. Results indicate that the energy eigenvalues are strongly correlated with the potential parameters. Using this potential to model mass spectra of charmonium and bottomonium, we show that results for the calculated quark mass spectra align closely with experimentally observed values.
  arXiv  Detail & Related papers  (2024-09-23T20:40:59Z)
• 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)
• Lattice Holography on a Quantum Computer [10.205744392217532]
  We compute the ground state of a spin system on a $(2+1)$-dimensional hyperbolic lattice. We observe that with achievable resources for coming quantum devices, the correlation function demonstrates an approximate scale-invariant behavior.
  arXiv  Detail & Related papers  (2023-12-16T21:48:24Z)
• Matter relative to quantum hypersurfaces [44.99833362998488]
  We extend the Page-Wootters formalism to quantum field theory. By treating hypersurfaces as quantum reference frames, we extend quantum frame transformations to changes between classical and nonclassical hypersurfaces.
  arXiv  Detail & Related papers  (2023-08-24T16:39:00Z)
• Quantum stochastic trajectories for particles and fields based on positive P-representation [0.0]
  We introduce a phase-space description based on the positive P representation for bosonic fields interacting with a system of quantum emitters. The formalism is applicable to collective light-matter interactions and open quantum systems with decoherence. A potential future application is the quantum mechanical description of collective spontaneous emission of an incoherently pumped ensemble of atoms.
  arXiv  Detail & Related papers  (2023-06-30T08:38:47Z)
• Independent-oscillator model and the quantum Langevin equation for an oscillator: A review [19.372542786476803]
  A derivation of the quantum Langevin equation is outlined based on the microscopic model of the heat bath. In the steady state, we analyze the quantum counterpart of energy equipartition theorem. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion.
  arXiv  Detail & Related papers  (2023-06-05T07:59:35Z)
• The Potential Inversion Theorem [0.0]
  We prove the potential inversion theorem, which says that wavefunction probability in these models is preserved under the sign inversion of the potential energy. We show how the potential inversion theorem illustrates several seemingly unrelated physical phenomena, including Bloch oscillations, localization, particle-hole symmetry, negative potential scattering, and magnetism.
  arXiv  Detail & Related papers  (2023-05-12T05:32:53Z)
• Partition of kinetic energy and magnetic moment in dissipative diamagnetism [20.218184785285132]
  We analyze dissipative diamagnetism, arising due to dissipative cyclotron motion in two dimensions, in the light of the quantum counterpart of energy equipartition theorem. The expressions for kinetic energy and magnetic moment are reformulated in the context of superstatistics.
  arXiv  Detail & Related papers  (2022-07-30T08:07:28Z)
• 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)
• Relativistic Motions of Spin-Zero Quantum Oscillator Field in a Global Monopole Space-Time with External Potential and AB-effect [0.0]
  We show that the obtained energy eigenvalues depend on the magnetic quantum flux which gives rise to the gravitational analog of the Aharonov-Bohm (AB) effect.
  arXiv  Detail & Related papers  (2022-02-28T08:52:09Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)

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.