scholarly journals A relativistic quantum theory of dyons wave propagation

2017 ◽  
Vol 95 (12) ◽  
pp. 1200-1207 ◽  
Author(s):  
B.C. Chanyal
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Quantum Theory ◽  
Quantum Electrodynamics ◽  
Wave Equations ◽  
Relativistic Quantum ◽  
Relativistic Wave Equation ◽  
Field Equations ◽  
Continuity Equations ◽  
Quantum Wave

Beginning with the quaternionic generalization of the quantum wave equation, we construct a simple model of relativistic quantum electrodynamics for massive dyons. A new quaternionic form of unified relativistic wave equation consisting of vector and scalar functions is obtained, and also satisfy the quaternionic momentum eigenvalue equation. Keeping in mind the importance of quantum field theory, we investigate the relativistic quantum structure of electromagnetic wave propagation of dyons. The present quantum theory of electromagnetism leads to generalized Lorentz gauge conditions for the electric and magnetic charge of dyons. We also demonstrate the universal quantum wave equations for two four-potentials as well as two four-currents of dyons. The generalized continuity equations for massive dyons in case of quantum fields are expressed. Furthermore, we concluded that the quantum generalization of electromagnetic field equations of dyons can be related to analogous London field equations (i.e., current to electromagnetic fields in and around a superconductor).

scholarly journals Some arguments for the wave equation in Quantum theory

2021 ◽  
Vol 5 (1) ◽  
pp. 314-336
Author(s):  
Tristram de Piro ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Quantum Theory ◽  
Continuity Equation ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Atomic System ◽  
Balmer Series ◽  
Inertial Frames ◽  
The Stability

We clarify some arguments concerning Jefimenko’s equations, as a way of constructing solutions to Maxwell’s equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial frames, which is intuitively reasonable for the stability of an atomic system, and prove that the condition is equivalent to the charge and current satisfying certain relations, including the wave equations. Finally, we prove that with these relations, the energy in the electromagnetic field is quantised and displays the properties of the Balmer series.

Approximation of pure acoustic seismic wave propagation in TTI media

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB97-WB107 ◽  
Author(s):  
Chunlei Chu ◽  
Brian K. Macy ◽  
Phil D. Anno
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Elastic Wave ◽  
Wave Equations ◽  
Computational Cost ◽  
P Wave ◽  
Anisotropy Axis ◽  
S Wave ◽  
Time Migration ◽  
Tti Media

Pseudoacoustic anisotropic wave equations are simplified elastic wave equations obtained by setting the S-wave velocity to zero along the anisotropy axis of symmetry. These pseudoacoustic wave equations greatly reduce the computational cost of modeling and imaging compared to the full elastic wave equation while preserving P-wave kinematics very well. For this reason, they are widely used in reverse time migration (RTM) to account for anisotropic effects. One fundamental shortcoming of this pseudoacoustic approximation is that it only prevents S-wave propagation along the symmetry axis and not in other directions. This problem leads to the presence of unwanted S-waves in P-wave simulation results and brings artifacts into P-wave RTM images. More significantly, the pseudoacoustic wave equations become unstable for anisotropy parameters [Formula: see text] and for heterogeneous models with highly varying dip and azimuth angles in tilted transversely isotropic (TTI) media. Pure acoustic anisotropic wave equations completely decouple the P-wave response from the elastic wavefield and naturally solve all the above-mentioned problems of the pseudoacoustic wave equations without significantly increasing the computational cost. In this work, we propose new pure acoustic TTI wave equations and compare them with the conventional coupled pseudoacoustic wave equations. Our equations can be directly solved using either the finite-difference method or the pseudospectral method. We give two approaches to derive these equations. One employs Taylor series expansion to approximate the pseudodifferential operator in the decoupled P-wave equation, and the other uses isotropic and elliptically anisotropic dispersion relations to reduce the temporal frequency order of the P-SV dispersion equation. We use several numerical examples to demonstrate that the newly derived pure acoustic wave equations produce highly accurate P-wave results, very close to results produced by coupled pseudoacoustic wave equations, but completely free from S-wave artifacts and instabilities.

Constitutive model and wave equations for linear, viscoelastic, anisotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 537-548 ◽  
Author(s):  
Jose M. Carcione
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Time Domain ◽  
Wave Equations ◽  
Superposition Principle ◽  
Fourier Method ◽  
Rock Properties ◽  
Orthorhombic Symmetry ◽  
Principal Axes ◽  
The Time Domain

Rocks are far from being isotropic and elastic. Such simplifications in modeling the seismic response of real geological structures may lead to misinterpretations, or even worse, to overlooking useful information. It is useless to develop highly accurate modeling algorithms or to naively use amplitude information in inversion processes if the stress‐strain relations are based on simplified rheologies. Thus, an accurate description of wave propagation requires a rheology that accounts for the anisotropic and anelastic behavior of rocks. This work presents a new constitutive relation and the corresponding time‐domain wave equation to model wave propagation in inhomogeneous anisotropic and dissipative media. The rheological equation includes the generalized Hooke’s law and Boltzmann’s superposition principle to account for anelasticity. The attenuation properties in different directions, associated with the principal axes of the medium, are controlled by four relaxation functions of viscoelastic type. A dissipation model that is consistent with rock properties is the general standard linear solid. This is based on a spectrum of relaxation mechanisms and is suitable for wavefield calculations in the time domain. One relaxation function describes the anelastic properties of the quasi‐dilatational mode and the other three model the anelastic properties of the shear modes. The convolutional relations are avoided by introducing memory variables, six for each dissipation mechanism in the 3-D case, two for the generalized SH‐wave equation, and three for the qP − qSV wave equation. Two‐dimensional wave equations apply to monoclinic and higher symmetries. A plane analysis derives expressions for the phase velocity, slowness, attenuation factor, quality factor and energy velocity (wavefront) for homogeneous viscoelastic waves. The analysis shows that the directional properties of the attenuation strongly depend on the values of the elasticities. In addition, the displacement formulation of the 3-D wave equation is solved in the time domain by a spectral technique based on the Fourier method. The examples show simulations in a transversely‐isotropic clayshale and phenolic (orthorhombic symmetry).

scholarly journals Quaternionic Approach to Dual Magnetohydrodynamics of Dyonic Cold Plasma

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
B. C. Chanyal ◽  
Mayank Pathak
Keyword(s):  
Wave Equation ◽  
Cold Plasma ◽  
Maxwell Equations ◽  
Magnetic Monopoles ◽  
Alfven Wave ◽  
Vorticity Field ◽  
Field Equations ◽  
Continuity Equations ◽  
Fields Equations ◽  
Quaternionic Formulation

The dual magnetohydrodynamics of dyonic plasma describes the study of electrodynamics equations along with the transport equations in the presence of electrons and magnetic monopoles. In this paper, we formulate the quaternionic dual fields equations, namely, the hydroelectric and hydromagnetic fields equations which are an analogous to the generalized Lamb vector field and vorticity field equations of dyonic cold plasma fluid. Further, we derive the quaternionic Dirac-Maxwell equations for dual magnetohydrodynamics of dyonic cold plasma. We also obtain the quaternionic dual continuity equations that describe the transport of dyonic fluid. Finally, we establish an analogy of Alfven wave equation which may generate from the flow of magnetic monopoles in the dyonic field of cold plasma. The present quaternionic formulation for dyonic cold plasma is well invariant under the duality, Lorentz, and CPT transformations.

scholarly journals A minimalist pilot-wave model for quantum electrodynamics

2007 ◽  
Vol 463 (2088) ◽  
pp. 3115-3129 ◽  
Author(s):  
W Struyve ◽  
H Westman
Keyword(s):  
Wave Function ◽  
Electromagnetic Field ◽  
Quantum Theory ◽  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Wave Model ◽  
Relativistic Quantum Theory ◽  
Pilot Wave ◽  
Free Electromagnetic Field

We present a way to construct a pilot-wave model for quantum electrodynamics. The idea is to introduce beables corresponding only to the bosonic and not to the fermionic degrees of freedom of the quantum state. We show that this is sufficient to reproduce the quantum predictions. The beables will be field beables corresponding to the electromagnetic field and will be introduced in a way similar to that of Bohm's model for the free electromagnetic field. Our approach is analogous to the situation in non-relativistic quantum theory, where Bell treated spin not as a beable but only as a property of the wave function. After presenting this model, we also discuss a simple way for introducing additional beables that represent the fermionic degrees of freedom.

scholarly journals AN AMBIGUOUS STATEMENT CALLED THE "TETRAD POSTULATE" AND THE CORRECT FIELD EQUATIONS SATISFIED BY THE TETRAD FIELDS

2005 ◽  
Vol 14 (12) ◽  
pp. 2095-2150 ◽  
Author(s):  
WALDYR A. RODRIGUES ◽  
QUINTINO A. G. SOUZA
Keyword(s):  
Wave Equation ◽  
Dirac Operator ◽  
Wave Equations ◽  
Point Of View ◽  
Field Equations ◽  
Hodge Laplacian ◽  
Clifford Bundle ◽  
Physics Literature ◽  
Laplacian Operators ◽  
Detailed Derivation

The names tetrad, tetrads, cotetrads have been used with many different meanings in the physics literature, not all of them equivalent from the mathematical point of view. In this paper, we introduce unambiguous definitions for each of those terms, and show how the old miscellanea made many authors introduce in their formalism an ambiguous statement called the "tetrad postulate," which has been the source of much misunderstanding, as we show explicitly by examining examples found in the literature. Since formulating Einstein's field equations intrinsically in terms of cotetrad fields θa, a = 0, 1, 2, 3 is a worthy enterprise, we derive the equation of motion of each θausing modern mathematical tools (the Clifford bundle formalism and the theory of the square of the Dirac operator). Indeed, we identify (giving all details and theorems) from the square of the Dirac operator some noticeable mathematical objects, namely, the Ricci, Einstein, covariant D'Alembertian and the Hodge Laplacian operators, which permit us to show that each θasatisfies a well-defined wave equation. Also, we present for completeness a detailed derivation of the cotetrad wave equations from a variational principle. We compare the cotetrad wave equation satisfied by each θawith some others appearing in the literature, and which are unfortunately in error.

scholarly journals Collision-space-time: Unified quantum gravity

2020 ◽  
Vol 33 (1) ◽  
pp. 46-78 ◽  
Author(s):  
Espen Gaarder Haug
Keyword(s):  
Wave Equation ◽  
Quantum Gravity ◽  
Planck Scale ◽  
Space Time ◽  
Relativistic Wave Equation ◽  
Relativistic Energy ◽  
Modern Physics ◽  
Heisenberg Uncertainty ◽  
Quantum Wave ◽  
New Formulation

For about hundred years, modern physics has not been able to build a bridge between quantum mechanics (QM) and gravity. However, a solution may be found here. We present our quantum gravity theory, which is rooted in indivisible particles where matter and gravity are related to collisions and can be described by collision-space-time. In this paper, we also show that we can formulate a quantum wave equation rooted in collision-space-time, which is equivalent to mass and energy. The beauty of our theory is that most of the main equations that currently exist in physics are, in general, not changed in terms of predictions and what we could call structural form, except at the Planck scale. The Planck scale is directly linked to gravity, which has obviously already been detected, and gravity is actually a Lorentz symmetry as well as a form of Heisenberg uncertainty break down at the Planck scale. Our theory gives a dramatic simplification of many physics formulas without altering the output predictions, except at the Planck scale, and this new formulation gives us a unified theory. The relativistic wave equation, the relativistic energy momentum relation, and Minkowski space can all be represented by simpler equations when we understand mass at a deeper level. This is not attained at a cost, but rather a reflection of the benefit in having gravity and QM unified under the same theory.

scholarly journals Quantum Theory of Gravitation

1998 ◽  
Vol 51 (3) ◽  
pp. 459
Author(s):  
H. S. Green
Keyword(s):  
Quantum Theory ◽  
Wave Equations ◽  
Algebraic Method ◽  
Empty Space ◽  
Space Time ◽  
Field Equations ◽  
Gauge Groups ◽  
Gravitational Field Equations ◽  
Non Euclidean Geometry ◽  
Curvature Tensors

It is possible to construct the non-euclidean geometry of space-time from the information carried by neutral particles. Points are identified with the quantal events in which photons or neutrinos are created and annihilated, and represented by the relativistic density matrices of particles immediately after creation or before annihilation. From these, matrices representing subspaces in any number of dimensions are constructed, and the metric and curvature tensors are derived by an elementary algebraic method; these are similar in all respects to those of Riemannian geometry. The algebraic method is extended to obtain solutions of Einstein’s gravitational field equations for empty space, with a cosmological term. General relativity and quantum theory are unified by the quantal embedding of non-euclidean space-time, and the derivation of a generalisation, consistent with Einstein"s equations, of the special relativistic wave equations of particles of any spin within representations of SO(3) ⊗ SO(4; 2). There are some novel results concerning the dependence of the scale of space-time on properties of the particles by means of which it is observed, and the gauge groups associated with gravitation.

NEW DEVELOPMENTS IN THE STUDY OFTIMEAS A QUANTUM OBSERVABLE

2008 ◽  
Vol 22 (12) ◽  
pp. 1877-1897 ◽  
Author(s):  
V. S. OLKHOVSKY ◽  
E. RECAMI
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Electrodynamics ◽  
Selfadjoint Operator ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
New Developments ◽  
Quantum Observable ◽  
Time In Quantum Mechanics

Some results are briefly reviewed and developments are presented on the study of Time in quantum mechanics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory. In particular, this paper deals with the hermitian (more precisely, maximal hermitian, but non-selfadjoint) operator for Time which appears: (i) for particles, in ordinary non-relativistic quantum mechanics; and (ii) for photons (i.e., in first-quantization quantum electrodynamics).

On the interaction of two electrons

1951 ◽  
Vol 208 (1095) ◽  
pp. 552-559 ◽  
Keyword(s):  
Wave Equation ◽  
Pair Production ◽  
Quantum Electrodynamics ◽  
Energy Levels ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Production Processes

A relativistic wave equation for helium-like systems which gives energy levels correct to within α 2 Ry is derived from quantum electrodynamics, care being taken in the handling of pair-production processes. Calculations made with it agree to this accuracy with Breit’s calculations.

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