Octonic massless field equations

2015 ◽  
Vol 30 (15) ◽  
pp. 1550084 ◽  
Author(s):  
Süleyman Demir ◽  
Murat Tanişli ◽  
Mustafa Emre Kansu
Keyword(s):  
Wave Equation ◽  
Field Equations ◽  
Real Component ◽  
Conservation Of Energy ◽  
Mathematical Structures ◽  
Massless Field ◽  
Energy Concept ◽  
Linear Gravity ◽  
Massless Fields ◽  
Generalized Wave Equation

In this paper, it is proven that the associative octons including scalar, pseudoscalar, pseudovector and vector values are convenient and capable tools to generalize the Maxwell–Dirac like field equations of electromagnetism and linear gravity in a compact and simple way. Although an attempt to describe the massless field equations of electromagnetism and linear gravity needs the sixteen real component mathematical structures, it is proved that these equations can be formulated in terms of eight components of octons. Furthermore, the generalized wave equation in terms of potentials is derived in the presence of electromagnetic and gravitational charges (masses). Finally, conservation of energy concept has also been investigated for massless fields.

scholarly journals Unification of massless field equations solutions for any spin

2021 ◽  
Author(s):  
Sergio Hojman ◽  
Felipe Asenjo
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Potential Functions ◽  
Field Equations ◽  
Fermionic Field ◽  
Massless Field ◽  
Coupled Equations ◽  
Klein Gordon ◽  
Fermionic Fields ◽  
Derivatives Of

Abstract A unification in terms of exact solutions for massless Klein–Gordon, Dirac, Maxwell, Rarita– Schwinger, Einstein, and bosonic and fermionic fields of any spin is presented. The method is based on writing all of the relevant dynamical fields in terms of products and derivatives of pre–potential functions, which satisfy d’Alambert equation. The coupled equations satisfied by the pre–potentials are non-linear. Remarkably, there are particular solutions of (gradient) orthogonal pre–potentials that satisfy the usual wave equation which may be used to construct exact non–trivial solutions to Klein–Gordon, Dirac, Maxwell, Rarita–Schwinger, (linearized and full) Einstein and any spin bosonic and fermionic field equations, thus giving rise to an unification of the solutions of all massless field equations for any spin. Some solutions written in terms of orthogonal pre–potentials are presented. Relations of this method to previously developed ones, as well as to other subjects in physics are pointed out.

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.

Perturbation analysis for massless spin fields in accelerating Kerr-Newman-(anti-)de Sitter black holes

2021 ◽  
pp. 2150175
Author(s):  
Hai-Bo Wei ◽  
Yi-Gu Chen ◽  
Hui Zheng ◽  
Zai-Dong Wang ◽  
Li-Qin Mi ◽  
...  
Keyword(s):  
Black Holes ◽  
Perturbation Theory ◽  
Wave Equation ◽  
Radial Function ◽  
De Sitter ◽  
Field Equations ◽  
Massless Spin ◽  
Spin Fields ◽  
Heun’S Equation ◽  
Massless Fields

We obtain the wave equation of the perturbation theory governing massless fields of spin 0, 1/2, 1, 3/2 and 2 in accelerating Kerr–Newman–(anti-)de Sitter black holes. We show that the wave equation is separable and the radial and angular equations can both be transformed into Heun’s equation. We approximate Heun’s equation and analyze the solution of radial function near the event horizon. It is worth pointing out that all the field equations collapse to a unique equation which means it can provide a possible way for the analog research between the gravitational field and those other fields.

scholarly journals Relativistic equations for elementary particles

1948 ◽  
Vol 192 (1029) ◽  
pp. 195-218 ◽  
Keyword(s):  
Elementary Particle ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Wave Form ◽  
Total Charge ◽  
Field Equations ◽  
Relativistic Approximation ◽  
Special Cases ◽  
Linear Differential

From the general principles of quantum mechanics it is deduced that the wave equation of a particle can always be written as a linear differential equation of the first order with matrix coefficients. The principle of relativity and the elementary nature of the particle then impose certain restrictions on these coefficient matrices. A general theory for an elementary particle is set up under certain assumptions regarding these matrices. Besides, two physical assumptions concerning the particle are made, namely, (i) that it satisfies the usual second-order wave equation with a fixed value of the rest mass, and (ii) either the total charge or the total energy for the particle-field is positive definite. It is shown that in consequence of (ii) the theory can be quantized in the interaction free case. On introducing electromagnetic interaction it is found that the particle exhibits a pure magnetic moment in the non-relativistic approximation. The well-known equations for the electron and the meson are included as special cases in the present scheme. As a further illustration of the theory the coefficient matrices corresponding to a new elementary particle are constructed. This particle is shown to have states of spin both 3/2 and 1/2. In a certain sense it exhibits an inner structure in addition to the spin. In the non-relativistic approximation the behaviour of this particle in an electromagnetic field is the same as that of the Dirac electron. Finally, the transition from the particle to the wave form of the equations of motion is effected and the field equations are given in terms of tensors and spinors.

An analytic signal based accurate time-domain visco-acoustic wave equation from the Constant-Q theory

Geophysics ◽  
2021 ◽  
pp. 1-58
Author(s):  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
Seismic Waves ◽  
Heterogeneous Media ◽  
Relaxation Property ◽  
Analytic Signal ◽  
Acoustic Wave Equation ◽  
Real Component ◽  
Frequency Components

We present a concise time-domain wave equation to accurately simulate wave propagation in visco-acoustic media. The central idea behind this work is to dismiss the negative frequency components from a time-domain signal by converting the signal to its analytic format. The negative frequency components of any analytic signal are always zero, meaning we can construct the visco-acoustic wave equation to honor the relaxation property of the media for positive frequencies only. The newly proposed complex-valued wave equation (CWE) represents the wavefield with its analytic signal, whose real part is the desired physical wavefield, while the imaginary part is the Hilbert transform of the real component. Specifically, this CWE is accurate for both weak and strong attenuating media in terms of both dissipation and dispersion and the attenuation is precisely linear with respect to the frequencies. Besides, the CWE is easy and flexible to model dispersion-only, dissipation-only or dispersion-plus-dissipation seismic waves. We have verified these CWEs by comparing the results with analytical solutions, and achieved nearly perfect matching. Except for the homogeneous Q media, we have also extended the CWEs to heterogeneous media. The results of the CWEs for heterogeneous Q media are consistent with those computed from the nonstationary operator based Fourier Integral method and from the Standard Linear Solid (SLS) equations.

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