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.

Symmetries, conservation laws, reductions, and exact solutions for the Klein–Gordon equation in de Sitter space–times

2012 ◽  
Vol 90 (7) ◽  
pp. 667-674 ◽  
Author(s):  
S. Jamal ◽  
A.H. Kara ◽  
Ashfaque H. Bokhari
Keyword(s):  
Dynamical Systems ◽  
Exact Solutions ◽  
Gordon Equation ◽  
De Sitter Space ◽  
Fundamental Solutions ◽  
De Sitter ◽  
Klein Gordon ◽  
Symmetry Generators ◽  
Math Phys ◽  
Klein Gordon Equation

In this paper, we complement the analysis involving the “fundamental” solutions of the Klein–Gordon equation in de Sitter space–times given by Yagdjian and A. Galstian (Comm. Math. Phys. 285, 293 (2009); Discrete and Continuous Dynamical Systems S, 2(3), 483 (2009)). Using the symmetry generators, we classify and reduce the underlying equations and show how this process may lead to exact solutions by quadratures.

scholarly journals FINITE ACTION KLEIN–GORDON SOLUTIONS ON LORENTZIAN MANIFOLDS

2006 ◽  
Vol 03 (07) ◽  
pp. 1349-1357 ◽  
Author(s):  
V. V. KOZLOV ◽  
I. V. VOLOVICH
Keyword(s):  
Mass Spectrum ◽  
Elliptic Equations ◽  
Gordon Equation ◽  
Infinite Family ◽  
De Sitter ◽  
Lorentzian Manifolds ◽  
Klein Gordon ◽  
Finite Action ◽  
Discrete Mass ◽  
Klein Gordon Equation

The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this paper we consider such a problem for the hyperbolic Klein–Gordon equation on Lorentzian manifolds. The investigation could help to answer the question why elementary particles have a discrete mass spectrum. An infinite family of square integrable solutions for the Klein–Gordon equation on the Friedman type manifolds is constructed. These solutions have a discrete mass spectrum and a finite action. In particular the solutions on de Sitter space are investigated.

ENTROPY OF SCHWARZSCHILD–de SITTER BLACK HOLE IN NON-THERMAL-EQUILIBRIUM

2001 ◽  
Vol 16 (11) ◽  
pp. 719-723 ◽  
Author(s):  
REN ZHAO ◽  
JUNFANG ZHANG ◽  
LICHUN ZHANG
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Thermal Equilibrium ◽  
Gordon Equation ◽  
Brick Wall ◽  
De Sitter ◽  
Logarithmic Term ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Wall Method

Starting from the Klein–Gordon equation, we calculate the entropy of Schwarzschild–de Sitter black hole in non-thermal-equilibrium by using the improved brick-wall method-membrane model. When taking the proper cutoff in the obtained result, we obtain that both black hole's entropy and cosmic entropy are proportional to the areas of event horizon. We avoid the logarithmic term and stripped term in the original brick-wall method. It offers a new way of studying the entropy of the black hole in non-thermal-equilibrium.

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 Relativistic scalar particle subject to a confining potential and Lorentz symmetry breaking effects in the cosmic string space–time

2016 ◽  
Vol 31 (07) ◽  
pp. 1650026 ◽  
Author(s):  
H. Belich ◽  
K. Bakke
Keyword(s):  
Symmetry Breaking ◽  
Cosmic String ◽  
Gordon Equation ◽  
Scalar Potential ◽  
Scalar Particle ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Klein Gordon ◽  
Lorentz Symmetry Breaking ◽  
Klein Gordon Equation

The behavior of a relativistic scalar particle subject to a scalar potential under the effects of the violation of the Lorentz symmetry in the cosmic string space–time is discussed. It is considered two possible scenarios of the Lorentz symmetry breaking in the CPT-even gauge sector of the Standard Model Extension defined by a tensor [Formula: see text]. Then, by introducing a scalar potential as a modification of the mass term of the Klein–Gordon equation, it is shown that the Klein–Gordon equation in the cosmic string space–time is modified by the effects of the Lorentz symmetry violation backgrounds and bound state solution to the Klein–Gordon equation can be obtained.

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