GORDON DECOMPOSITION OF DIRAC SPINORS IN GRAVITATIONAL BACKGROUND

1992 ◽  
Vol 07 (19) ◽  
pp. 1707-1714
Author(s):  
D. PARASHAR
Keyword(s):  
Gordon Equation ◽  
Curved Space ◽  
Walker Metric ◽  
Klein Gordon ◽  
Space Formalism ◽  
The Universe ◽  
Dirac Current ◽  
Dirac Spinors ◽  
Klein Gordon Equation ◽  
Gravitational Background

The scheme outlined earlier is continued here to investigate the structure of Dirac spinors in the background of a gravitational field within the context of cosmological Robertson-Walker metric where the treatment is based on general considerations of spatially curved (non-flat) hypersurfaces embracing open as well as closed versions of the Universe. A Gordon decomposition of the generalized Dirac current is then carried out in terms of the polarization and the magnetization densities. We also take a look at the Klein-Gordon equation in the curved space formalism.

scholarly journals Klein–Gordon equation in curved space-time

2018 ◽  
Vol 39 (4) ◽  
pp. 045405 ◽  
Author(s):  
R D Lehn ◽  
S S Chabysheva ◽  
J R Hiller
Keyword(s):  
Gordon Equation ◽  
Space Time ◽  
Curved Space ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals From Fock’s transformation to de Sitter space

2015 ◽  
Vol 93 (7) ◽  
pp. 734-737 ◽  
Author(s):  
T. Foughali ◽  
A. Bouda
Keyword(s):  
Coordinate Transformation ◽  
Gordon Equation ◽  
De Sitter Space ◽  
Space Time ◽  
Poisson Brackets ◽  
De Sitter ◽  
Deformed Algebra ◽  
Klein Gordon ◽  
The Universe ◽  
Klein Gordon Equation

As with Deformed Special Relativity, we showed recently that the Fock coordinate transformation can be derived from a new deformed Poisson brackets. This approach allowed us to establish the corresponding momentum transformation that keeps invariant the four-dimensional contraction pμxμ. From the resulting deformed algebra, we construct the corresponding first Casimir. After first quantization, we show by using the Klein–Gordon equation that the space-time of the Fock transformation is the de Sitter one. As we will see, the invariant length representing the universe radius in the space-time of Fock’s transformation is exactly the radius of the embedded hypersurface representing the de Sitter space-time.

scholarly journals Scalar-field theory of dark matter

2014 ◽  
Vol 29 (13) ◽  
pp. 1450074 ◽  
Author(s):  
Kerson Huang ◽  
Chi Xiong ◽  
Xiaofei Zhao
Keyword(s):  
Dark Matter ◽  
Scalar Field ◽  
Gordon Equation ◽  
Galactic Halo ◽  
Galactic Rotation ◽  
Klein Gordon ◽  
External Sources ◽  
Galaxy Collisions ◽  
The Universe ◽  
Klein Gordon Equation

We develop a theory of dark matter based on a previously proposed picture, in which a complex vacuum scalar field makes the universe a superfluid, with the energy density of the superfluid giving rise to dark energy, and variations from vacuum density giving rise to dark matter. We formulate a nonlinear Klein–Gordon equation to describe the superfluid, treating galaxies as external sources. We study the response of the superfluid to the galaxies, in particular, the emergence of the dark-matter galactic halo, contortions during galaxy collisions and the creation of vortices due to galactic rotation.

HIGHER-DIMENSIONAL GEOMETRIC DESCRIPTION OF THE QUANTUM KLEIN–GORDON EQUATION

2013 ◽  
Vol 10 (09) ◽  
pp. 1320014 ◽  
Author(s):  
BENJAMIN KOCH
Keyword(s):  
Electromagnetic Field ◽  
Gordon Equation ◽  
Bohmian Mechanics ◽  
External Electromagnetic Field ◽  
Geometrical Theory ◽  
Geometric Description ◽  
Curved Space ◽  
Higher Dimensional ◽  
Klein Gordon ◽  
Klein Gordon Equation

It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum mechanics as a purely classical geometrical theory. The results are further generalized to interactions with an external electromagnetic field.

Klein–Gordon equation with four inverse power term potentials

2020 ◽  
Vol 35 (11) ◽  
pp. 2050080 ◽  
Author(s):  
E. Anemena Etoga ◽  
J. M. Ema’a Ema’a ◽  
P. Ele Abiama ◽  
G. H. Ben-Bolie
Keyword(s):  
Energy Equation ◽  
Gordon Equation ◽  
Inverse Power ◽  
Generic Model ◽  
Relativistic Energy ◽  
Heun Function ◽  
Special Cases ◽  
Klein Gordon ◽  
The Universe ◽  
Klein Gordon Equation

To describe interactions in the universe in a more realistic way, we used the generic model of Klein–Gordon equation with four inverse power term potentials. Using bi-confluent Heun function, we obtained a transcendental energy equation and the wave function. Moreover, we determined the non-relativistic energy. Special cases of the potential have also been discussed. These results obtained are highly applicable in many branches of physics and life sciences.

SOLUTION OF THE KLEIN–GORDON EQUATION IN A 2 + 1 CURVED SPACE–TIME

2001 ◽  
Vol 16 (18) ◽  
pp. 1151-1156
Author(s):  
TINA A. HARRIOTT ◽  
J. G. WILLIAMS
Keyword(s):  
Scalar Field ◽  
Bessel Functions ◽  
Gordon Equation ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Whittaker Functions ◽  
Curved Space ◽  
Standard Manner ◽  
Klein Gordon ◽  
Klein Gordon Equation

The Klein–Gordon equation for a massless scalar field is considered for an extended matter source in 2 + 1 dimensions. It is shown how a solution can be found using Whittaker functions and can be normalized in the standard manner. In the point source limit, the solution reduces to the usual expression in terms of Bessel functions.

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