scholarly journals Klein-Gordon-Fock equation from Einstein general relativity

2016 ◽  
Vol 26 (2) ◽  
pp. 181
Author(s):  
Vo Van Thuan
Keyword(s):  
General Relativity ◽  
Gravitational Equation ◽  
Hubble Expansion ◽  
Time Space ◽  
Weak Space ◽  
Exponential Solution ◽  
Klein Gordon ◽  
Space Symmetry ◽  
Original Time ◽  
Einstein Gravitational Equation

A time-space symmetry based cylindrical model of geometrical dynamics was proposed. Accordingly, the solution of Einstein gravitational equation in vacuum has a duality: an exponential solution and a wave-like one.  The former leads to a "microscopic" cosmological model with Hubble expansion. Due to interaction of a Higgs-like cosmological potential, the original time-space symmetry is spontaneously broken, inducing a strong time-like curvature and a weak space-like deviation curve.  In the result, the wave-like solution leads  to Klein-Gordon-Fock equation which would serve  an explicit approach to the problem of consistency between quantum mechanics and general relativity.

scholarly journals The Modern Induced Matter Approach of General Relativity for Quantum Mechanics

2017 ◽  
Vol 26 (3) ◽  
pp. 209
Author(s):  
Vo Van Thuan ◽  
Nguyen Thi Kim Thoa
Keyword(s):  
Quantum Mechanics ◽  
Physical Reality ◽  
Space Time ◽  
Gravitational Equation ◽  
Hubble Expansion ◽  
Higher Dimensional ◽  
Matter Theory ◽  
Klein Theory ◽  
Klein Gordon ◽  
Induced Matter

Wesson and his co-workers developed so-called space-time-matter theory (5D-STM) as a generalization of Kaluza-Klein theory, where the extra-dimension in the 5D space-time is no more compacted, but keeping extended in a macroscopic scale to describe the properties of matter in 4D physics. In a trend of 5D-STM approach (or the induced-matter theory), following a bi-cylindrical model of geometrical dynamics, a recent study has shown that the higher 6D-dimensional gravitational equation leads to bi-geodesic description in an extended timespace symmetry which fits Hubble expansion in a ”microscopic” cosmological model. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles. The 4D-embedded dual solutions of the higher dimensional gravitational equation could shed light on origin of physical reality in quantum mechanics, which is to compare with the achievements of the 5D-STM theory.

scholarly journals COLLECTIVE AND RELATIVE VARIABLES FOR A CLASSICAL KLEIN–GORDON FIELD

1999 ◽  
Vol 14 (21) ◽  
pp. 3387-3420 ◽  
Author(s):  
G. LONGHI ◽  
M. MATERASSI
Keyword(s):  
General Relativity ◽  
Asymptotic Behavior ◽  
Harmonic Analysis ◽  
Momentum Space ◽  
Conserved Quantities ◽  
Canonical Transformations ◽  
Collective Variables ◽  
Klein Gordon ◽  
Definition Of

In this paper a set of canonical collective variables is defined for a classical Klein–Gordon field and the problem of the definition of a set of canonical relative variables is discussed. This last point is approached by means of a harmonic analysis in momentum space. This analysis shows that the relative variables can be defined if certain conditions are fulfilled by the field configurations. These conditions are expressed by the vanishing of a set of conserved quantities, referred to as supertranslations since as canonical observables they generate a set of canonical transformations whose algebra is the same as that which arises in the study of the asymptotic behavior of the metric of an isolated system in General Relativity.9

scholarly journals Implementation of a Quantized Line Element in Klein-Gordon and Dirac Fields

2015 ◽  
Vol 48 ◽  
pp. 68-86
Author(s):  
D.L. Bulathsinghala ◽  
K.A.I.L. Wijewardena Gamalath
Keyword(s):  
Dirac Equation ◽  
Gordon Equation ◽  
Line Element ◽  
Coarse Grained ◽  
Relativistic Energy ◽  
Time Intervals ◽  
Quantization Rule ◽  
Time Space ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper an ansatz that the anti-commutation rules hold only as integrated average over time intervals and not at every instant giving rise to a time-discrete form of Klein-Gordon equation is examined. This coarse-grained validation of the anti-commutation rules enables us to show that the relativistic energy-momentum relation holds only over discrete time intervals, fitting well with the time-energy uncertainty relation. When this time-discrete scheme is applied to four vector notations in relativity, the line-element can be quantized and thereby how the physical attributes associated with time, space and matter can be quantized is sketched. This potentially enables us to discuss the Zeno’s arrow paradox within the classical limit. As the solutions of the Dirac equation can be used to construct solutions to the Klein-Gordon equation, this temporal quantization rule is applied to the Dirac equation and the solutions associated with the Dirac equation under such conditions are interpreted. Finally, the general relativistic effects are introduced to a line-element associated with a particle in relativistic motion and a time quantized line-element associated with gravity is obtained.

scholarly journals Modified general relativity and quantum theory in curved spacetime

2021 ◽  
Author(s):  
Gary Nash
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Momentum Tensor ◽  
Space Time ◽  
Lie Derivative ◽  
Dirac Spinor ◽  
Outer Product ◽  
Klein Gordon ◽  
Hermitian Conjugate ◽  
Quantum Vector

With appropriate modifications, the multi-spin Klein–Gordon (KG) equation of quantum field theory can be adapted to curved space–time for spins 0, 1, 1/2. The associated particles in the microworld then move as a wave at all space–time coordinates. From the existence in a Lorentzian space–time of a line element field [Formula: see text], the spin-1 KG equation [Formula: see text] is derived from an action functional involving [Formula: see text] and its covariant derivative. The spin-0 KG equation and the KG equation of the outer product of a spin-1/2 Dirac spinor and its Hermitian conjugate are then constructed. Thus, [Formula: see text] acts as a fundamental quantum vector field. The symmetric part of the spin-1 KG equation, [Formula: see text], is the Lie derivative of the metric. That links the multi-spin KG equation to Modified General Relativity (MGR) through its energy–momentum tensor of the gravitational field. From the invariance of the action functionals under the diffeomorphism group Diff(M), which is not restricted to the Lorentz group, [Formula: see text] can instantaneously transmit information along [Formula: see text]. That establishes the concept of entanglement within a Lorentzian formalism. The respective local/nonlocal characteristics of MGR and quantum theory no longer present an insurmountable problem to unify the theories.

scholarly journals Gravitational decoupling of generalized Horndeski hybrid stars

2022 ◽  
Vol 82 (1) ◽  
Author(s):  
Roldao da Rocha
Keyword(s):  
General Relativity ◽  
Physical Properties ◽  
Neutron Stars ◽  
Observational Data ◽  
White Dwarfs ◽  
Mass Function ◽  
Effective Radius ◽  
Asymptotic Value ◽  
Klein Gordon ◽  
Hybrid Stars

AbstractGravitational decoupled compact polytropic hybrid stars are here addressed in generalized Horndeski scalar-tensor gravity. Additional physical properties of hybrid stars are scrutinized and discussed in the gravitational decoupling setup. The asymptotic value of the mass function, the compactness, and the effective radius of gravitational decoupled hybrid stars are studied for both cases of a bosonic and a fermionic prevalent core. These quantities are presented and discussed as functions of Horndeski parameters, the decoupling parameter, the adiabatic index, and the polytropic constant. Important corrections to general relativity and generalized Horndeski scalar-tensor gravity, induced by the gravitational decoupling, comply with available observational data. Particular cases involving white dwarfs, boson stellar configurations, neutron stars, and Einstein–Klein–Gordon solutions, formulated in the gravitational decoupling context, are also scrutinized.

Icosahedral Symmetry: A Review

2015 ◽  
Vol 5 ◽  
pp. 1-8
Author(s):  
J.A. de Wet
Keyword(s):  
Elementary Particle ◽  
Particle Physics ◽  
Riemann Surfaces ◽  
W Bosons ◽  
Icosahedral Symmetry ◽  
Gravitational Equation ◽  
Elementary Particle Physics ◽  
Algebraic Representations ◽  
Einstein Gravitational Equation ◽  
Over 40 Years

This Review covers over 40 years of research on using the algebras of Quarternions E6;E8to model Elementary Particle physics. In particular the Binary Icosahedral group is isomorphic to theExceptional Lie algebra E8 by the MacKay correspondence. And the toric graph of E8 in Fig.2 with240 vertices on 4 binary Riemann surfaces each carrying 60 vertices, models a solution of the Ernstequation for the stationary symmetric Einstein gravitational equation. Furthermore the 15 synthemesof E8, consisting of 5 sets of 3,can be identified with algebraic representations of the nucleon,supersymmetric particles,W bosons and Dark Matter.

INTERACTING THIRD QUANTIZED GENERAL RELATIVITY AND CHANGE OF TOPOLOGY

1993 ◽  
Vol 08 (20) ◽  
pp. 1849-1858 ◽  
Author(s):  
YOAV PELEG
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Dynamical Equation ◽  
Physical Space ◽  
Positive Definite ◽  
Curved Space ◽  
Infinite Dimensional ◽  
The Third ◽  
Klein Gordon ◽  
Interaction Term

The Wheeler-DeWitt equation can be treated as a dynamical equation of a field theory on superspace, which is a free Klein-Gordon field (in an infinite-dimensional curved space) with a non-positive-definite mass squared term. This suggests that one should add an interaction term to the third quantized theory, and by that to get a Hamiltonian which is bounded from below. This process may allow a change of topology. A consistent third quantized theory can be defined in a subspace of superspace for which the Ricci scalar is zero. We consider a simple example of such subspace, and examine (in it) two kinds of interactions, one which is local in superspace and one which is local in the physical space.

scholarly journals The spacetime between Einstein and Kaluza–Klein

2020 ◽  
Vol 35 (36) ◽  
pp. 2030020
Author(s):  
Chris Vuille
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Differential Operators ◽  
Mathematical Structure ◽  
Field Equations ◽  
Five Dimensions ◽  
Four Dimensions ◽  
Klein Theory ◽  
Klein Gordon ◽  
Kaluza Klein

In this paper I introduce tensor multinomials, an algebra that is dense in the space of nonlinear smooth differential operators, and use a subalgebra to create an extension of Einstein’s theory of general relativity. In a mathematical sense this extension falls between Einstein’s original theory of general relativity in four dimensions and the Kaluza–Klein theory in five dimensions. The theory has elements in common with both the original Kaluza–Klein and Brans–Dicke, but emphasizes a new and different underlying mathematical structure. Despite there being only four physical dimensions, the use of tensor multinomials naturally leads to expanded operators that can incorporate other fields. The equivalent Ricci tensor of this geometry is robust and yields vacuum general relativity and electromagnetism, as well as a Klein–Gordon-like quantum scalar field. The formalism permits a time-dependent cosmological function, which is the source for the scalar field. I develop and discuss several candidate Lagrangians. Trial solutions of the most natural field equations include a singularity-free dark energy dust cosmology.

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