The Dirac Equation in a Gravitational Field

2016 ◽  
pp. 261-273
Author(s):  
Maurizio Gasperini
Keyword(s):  
Gravitational Field ◽  
Dirac Equation

scholarly journals The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Alexander Burinskii
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Higgs Field ◽  
Vacuum State ◽  
Relativistic String ◽  
Dirac Equations ◽  
Dirac Electron ◽  
Relativistic Scattering

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation

2016 ◽  
Vol 71 (1) ◽  
pp. 53-57 ◽  
Author(s):  
Friedwardt Winterberg
Keyword(s):  
Gravitational Field ◽  
Dirac Equation ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Negative Energy ◽  
Quantum Mechanical ◽  
Field Equations ◽  
Negative Mass ◽  
Pilot Wave ◽  
Extended Theories Of Gravity

AbstractAn explanation of the quantum-mechanical particle-wave duality is given by the watt-less emission of gravitational waves from a particle described by the Dirac equation. This explanation is possible through the existence of negative energy, and hence negative mass solutions of Einstein’s gravitational field equations. They permit to understand the Dirac equation as the equation for a gravitationally bound positive–negative mass (pole–dipole particle) two-body configuration, with the mass of the Dirac particle equal to the positive mass of the gravitational field binding the positive with the negative mass particle, and with the mass particles making a luminal “Zitterbewegung” (quivering motion), emitting a watt-less oscillating positive–negative space curvature wave. It is shown that this thusly produced “Zitterbewegung” reproduces the quantum potential of the Madelung-transformed Schrödinger equation. The watt-less gravitational wave emitted by the quivering particles is conjectured to be de Broglie’s pilot wave. The hypothesised connection of the Dirac equation to gravitational wave physics could, with the failure to detect gravitational waves by the LIGO antennas and pulsar timing arrays, give a clue to extended theories of gravity, or a correction of astrophysical models for the generation of such waves.

Dirac Field, Gravity, Inertial Effects, and Computer Algebra

1997 ◽  
Vol 08 (02) ◽  
pp. 345-359 ◽  
Author(s):  
Dumitru N. Vulcanov ◽  
Ion I. Cotăescu
Keyword(s):  
Gravitational Field ◽  
Dirac Equation ◽  
Reference Frame ◽  
Computer Algebra ◽  
Dirac Field ◽  
Inertial Reference Frame ◽  
Inertial Effects ◽  
Algebraic Programming ◽  
Relativistic Approximation

The article presents some new results obtained for the non-relativistic approximation of the Dirac equation in a non-inertial reference frame — rotated and accelerated — and in Schwarzschild gravitational field. These results are obtained with new routines of algebraic programming in REDUCE + EXCALC language for the Dirac equation in a non-inertial reference frame and after three successive Foldy–Wouthuysen transformations.

INFLUENCE OF THE GRAVITATIONAL FIELD ON THE QUANTUM STATES OF THE ELECTRON IN A PENNING TRAP

1996 ◽  
Vol 11 (17) ◽  
pp. 1429-1443
Author(s):  
R. STAUDT ◽  
U.E. SCHRÖDER
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Penning Trap ◽  
Energy Levels ◽  
Quantum States ◽  
Minimal Coupling ◽  
Relative Shift ◽  
The Earth ◽  
Resulting Effect

Starting from the general covariant Dirac equation with minimal coupling of an electromagnetic field the corrections to the energy levels of the electron in a Penning trap caused by the gravitational field of the Earth are computed. Our discussion shows that the resulting effect is detectable only at the specific eigenfrequencies of the electron. The relative shift of these frequencies due to the gravitational field is found to be 2.1×10–9. It is briefly indicated how this effect in principle could be observed in suitable experiments performed with higher precision.

Exact solution of the Dirac equation for a Coulomb and scalar potentials in the gravitational field of a cosmic string

2005 ◽  
Vol 341 (1-4) ◽  
pp. 39-47 ◽  
Author(s):  
Geusa de A. Marques ◽  
Valdir B. Bezerra ◽  
Sandro G. Fernandes
Keyword(s):  
Exact Solution ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Cosmic String ◽  
Scalar Potentials

Generalized Dirac Equation for a particle in a gravitational field

2021 ◽  
Vol 53 (7) ◽  
Author(s):  
Daniel Chemisana ◽  
Jaume Giné ◽  
Jaime Madrid
Keyword(s):  
Gravitational Field ◽  
Dirac Equation ◽  
Generalized Dirac Equation
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