Spaces of positive and negative frequency solutions of field equations in curved space–times. I. The Klein–Gordon equation in stationary space–times

1977 ◽  
Vol 18 (11) ◽  
pp. 2153-2161 ◽  
Author(s):  
Carlos Moreno
Keyword(s):  
Gordon Equation ◽  
Field Equations ◽  
Curved Space ◽  
Klein Gordon ◽  
Klein Gordon Equation

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 Solitons for the Nonlinear Klein-Gordon Equation

2010 ◽  
Vol 10 (2) ◽  
Author(s):  
J. Bellazzini ◽  
V. Benci ◽  
C. Bonanno ◽  
A.M. Micheletti
Keyword(s):  
Solitary Waves ◽  
Gordon Equation ◽  
Energy Charge ◽  
Sufficient Conditions ◽  
Orbital Stability ◽  
Field Equations ◽  
Klein Gordon ◽  
Ratio Energy ◽  
Klein Gordon Equation

AbstractIn this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we are interested in sufficient conditions on the potential for the existence of solitons. Our proof is based on the study of the ratio energy/charge of a function, which turns out to be a useful approach for many field equations.

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

OCTONIC GRAVITATIONAL FIELD EQUATIONS

2013 ◽  
Vol 28 (21) ◽  
pp. 1350112 ◽  
Author(s):  
SÜLEYMAN DEMİR ◽  
MURAT TANIŞLI ◽  
TÜLAY TOLAN
Keyword(s):  
Wave Equation ◽  
Gordon Equation ◽  
The Other ◽  
Massive Graviton ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Number Systems ◽  
Klein Gordon ◽  
Linear Gravity ◽  
Klein Gordon Equation

Generalized field equations of linear gravity are formulated on the basis of octons. When compared to the other eight-component noncommutative hypercomplex number systems, it is demonstrated that associative octons with scalar, pseudoscalar, pseudovector and vector values present a convenient and capable tool to describe the Maxwell–Proca-like field equations of gravitoelectromagnetism in a compact and simple way. Introducing massive graviton and gravitomagnetic monopole terms, the generalized gravitational wave equation and Klein–Gordon equation for linear gravity are also developed.

scholarly journals The Euler-Lagrange expression and degenerate lagrange densities

1972 ◽  
Vol 14 (4) ◽  
pp. 482-495 ◽  
Author(s):  
D. Lovelock
Keyword(s):  
Variational Principle ◽  
Fourth Order ◽  
Gordon Equation ◽  
Einstein Equations ◽  
Theoretical Physics ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Lagrange Equations ◽  
Klein Gordon ◽  
Klein Gordon Equation

It is well known that many of the field equations from theoretical physics (e.g. Einstein field equations, Maxwell's equations, Klein-Gordon equation) can be obtained from a variational principle with a suitably chosen Lagrange density. In the case of the Einstein equations the corresponding Lagrangian is degenerate (i.e., the associated Euler-Lagrange equations are of second order whereas in general these would be of fourth order), while in the cases of the Maxwell and Klein-Gordon equations the Lagrangian usually used is not degenerate.

Zur einheitlichen Feldtheorie

1964 ◽  
Vol 19 (4) ◽  
pp. 401-405
Author(s):  
G. Braunss
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Field Equations ◽  
Bianchi Identities ◽  
Euclidean Metric ◽  
Klein Gordon ◽  
Klein Gordon Equation

The basic conception of this paper is the assumption, that all quantities characterizing the metric are functionals of one field (worldfield). For the sake of mathematical simplicity a scalar field Φ is considered. The investigations are based on the following system of field equations:Rmn - ½ gmn R=½ gmn [gabΦ, aΦ, b + F(Φ)]-Φ,mΦ, n;F is a functional of Φ. According to the basic conception only such solutions for the gmn are permitted, which for Φ ≡ 0 give the corresponding values of a euclidean metric. Due to the BIANCHI-identities it follows as a consequence of the field equations, that Φ satisfies a nonlinear KLEIN-GORDON-equation :gabΦ;ab-½(dF/dΦ) =0 .The conditions for a nonsingular, static and centralsymmetrical solution are investigated. With regard to cosmological problems the equations for a conformal-flat, timedependent metric are discussed.

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.

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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