Charged spinor solitons

1986 ◽  
Vol 64 (3) ◽  
pp. 232-238 ◽  
Author(s):  
P. Mathieu ◽  
T. F. Morris
Keyword(s):  
Dirac Equation ◽  
Mass Parameter ◽  
Structure Constant ◽  
Finite Energy ◽  
Stationary Solutions ◽  
Fine Structure Constant ◽  
Many Body ◽  
Nonlinear Dirac Equation ◽  
Frequency Relation ◽  
Static Energy

A nonlinear Dirac equation for which all finite-energy stationary solutions are nontopological solitons with compact support is coupled to the electromagnetic field. In a many-body situation, it is shown that the equilibrium is reached when all the solitons have the same value of the charge. This implies the de Broglie frequency relation and a relation for the fine-structure constant. In specific domains and to a very good approximation, the model reduces to the linear Dirac equation for a particle whose mass parameter is the static energy of the soliton.

scholarly journals Space Dimension Renormdynamics

Particles ◽  
2020 ◽  
Vol 3 (2) ◽  
pp. 364-379
Author(s):  
Martin Bures ◽  
Nugzar Makhaldiani
Keyword(s):  
Point Charge ◽  
Hamiltonian Dynamics ◽  
Mass Parameter ◽  
Structure Constant ◽  
Physical Models ◽  
Fine Structure Constant ◽  
Cornell Potential ◽  
Unified Field ◽  
Charge Potential ◽  
Spatial Dimensions

We aim to construct a potential better suited for studying quarkonium spectroscopy. We put the Cornell potential into a more geometrical setting by smoothly interpolating between the observed small and large distance behaviour of the quarkonium potential. We construct two physical models, where the number of spatial dimensions depends on scale: one for quarkonium with Cornell potential, another for unified field theories with one compactified dimension. We construct point charge potential for different dimensions of space. The same problem is studied using operator fractal calculus. We describe the quarkonium potential in terms of the point charge potential and identify the strong coupling fine structure constant dynamics. We formulate renormdynamics of the structure constant in terms of Hamiltonian dynamics and solve the corresponding motion equations by numerical and graphical methods, we find corresponding asymptotics. Potentials of a nonlinear extension of quantum mechanics are constructed. Such potentials are ingredients of space compactification problems. Mass parameter effects are motivated and estimated.

Reply to "A remark on Moore's new method of obtaining approximate solutions of the Dirac equation"

1981 ◽  
Vol 59 (11) ◽  
pp. 1614-1619 ◽  
Author(s):  
R. A. Moore ◽  
Sam Lee
Keyword(s):  
Dirac Equation ◽  
Structure Constant ◽  
Approximate Solutions ◽  
Wave Functions ◽  
Fine Structure Constant ◽  
Energy Calculation ◽  
Calculation Error ◽  
First Order ◽  
The One ◽  
The Individual

This work was written to clarify the use of a recently developed procedure to obtain approximate solutions of the one-particle Dirac equation directly and in response to a recent critique on its application to lowest order. The critique emphasized the fact that when the wave functions are determined only to zero order then a first order energy calculation contains significant errors of the order of α4, α being the fine structure constant, and a matrix element calculation error of order α2. Tomishima re-affirms that higher order solutions are required to obtain accuracy of these orders. In this work the hierarchy of equations occurring in the procedure is extended to first order and it is shown that exact solutions exist for hydrogen-like atoms. It is also shown that the energy in second order contains all of the contributions of order α4. In addition, we illustrate, in detail, that the procedure can be aplied in such a way as to isolate the individual components of the wave functions and energies as power series of α2. This analysis lays the basis for the determination of suitable numerical methods and hence for application to physical systems.

Many-Body Stability Implies a Bound on the Fine-Structure Constant

1988 ◽  
Vol 61 (15) ◽  
pp. 1695-1697 ◽  
Author(s):  
Elliott H. Lieb ◽  
Horng-Tzer Yau
Keyword(s):  
Fine Structure ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Many Body

scholarly journals Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Sébastien Léger ◽  
Javier Puertas-Martínez ◽  
Karthik Bharadwaj ◽  
Rémy Dassonneville ◽  
Jovian Delaforce ◽  
...  
Keyword(s):  
Casimir Effect ◽  
Structure Constant ◽  
Zero Point ◽  
Fine Structure Constant ◽  
Many Body ◽  
Bloch Oscillations ◽  
Superconducting Circuits ◽  
High Impedance ◽  
Non Linear ◽  
Large Phase

AbstractElectromagnetic fields possess zero point fluctuations which lead to observable effects such as the Lamb shift and the Casimir effect. In the traditional quantum optics domain, these corrections remain perturbative due to the smallness of the fine structure constant. To provide a direct observation of non-perturbative effects driven by zero point fluctuations in an open quantum system we wire a highly non-linear Josephson junction to a high impedance transmission line, allowing large phase fluctuations across the junction. Consequently, the resonance of the former acquires a relative frequency shift that is orders of magnitude larger than for natural atoms. Detailed modeling confirms that this renormalization is non-linear and quantum. Remarkably, the junction transfers its non-linearity to about thirty environmental modes, a striking back-action effect that transcends the standard Caldeira-Leggett paradigm. This work opens many exciting prospects for longstanding quests such as the tailoring of many-body Hamiltonians in the strongly non-linear regime, the observation of Bloch oscillations, or the development of high-impedance qubits.

Perturbation Methods

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Fine Structure ◽  
Dirac Equation ◽  
Perturbation Methods ◽  
Relativistic Quantum ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Perturbation Expansions ◽  
Relativistic Corrections

Perturbation theory has been one of the most frequently used and most powerful tools of quantum mechanics. The very foundations of relativistic quantum theory—quantum electrodynamics—are perturbative in nature. Many-body perturbation theory has been used for electron correlation treatments since the early days of quantum chemistry, and in more recent times multireference perturbation theories have been developed to provide quantitative or semiquantitative information in very complex systems. In the beginnings of relativistic quantum mechanics, perturbation methods based on an expansion in powers of the fine structure constant, α = 1/c, were used extensively to obtain operators that would provide a connection with nonrelativistic quantum mechanics and permit some evaluation of relativistic corrections, in days well before the advent of the computer. This seems a reasonable approach, considering the small size of the fine structure constant—and for light elements it has been found to work remarkably well. Relativity is a small perturbation for a good portion of the periodic table. Perturbation expansions have their limitations, however, and as well as successes, there have been failures due to the highly singular or unbounded nature of the operators in the perturbation expansions. Therefore, in recent times other perturbation approaches have been developed to provide alternatives to the standard Breit–Pauli approach. This chapter is devoted to the development of perturbation expansions in powers of 1/c from the Dirac equation. In the previous chapter, the Pauli Hamiltonian was developed using the Foldy–Wouthuysen transformation. While this is an elegant method, it is probably simpler to make the derivation from the elimination of the small component with expansion of the denominator, and it is this approach that we use here. Another convenient approach is to make use of the modified Dirac equation in the limit of equality of the large and pseudo-large components. This approach enables us to draw on results from the modified Dirac approach in developing the two-electron terms of the Breit–Pauli Hamiltonian. We then demonstrate how the use of perturbation theory for relativistic corrections requires that multiple perturbation theory be employed for correlation effects and for properties.

scholarly journals The Anomalous Magnetic Moment of the Electron and Proton Cores According to the Planck Vacuum Theory

2019 ◽  
Vol 4 (6) ◽  
pp. 117-119
Author(s):  
William C. Daywitt
Keyword(s):  
Fine Structure ◽  
Dirac Equation ◽  
Quantum Electrodynamic ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
The Relationship ◽  
Vacuum Theory ◽  
The Invisible

Despite the resounding success of the quantum electrodynamic (QED) calculations, there remains some confusion concerning the Dirac equation’s part in the calculation of the anomalous magnetic moment of the electron and proton. The confusion resides in the nature of the Dirac equation, the fine structure constant, and the relationship between the two. This paper argues that the Dirac equation describes the coupling of the electron or proton cores to the invisible Planck vacuum (PV) state (involving e2 ); and that the fine structure constant ( = e2/e2 ) connects that equation to the electron or proton particles measured in the laboratory (involving e2).

An Alternative Method of Obtaining Approximate Solutions to the Dirac Equation. I

1975 ◽  
Vol 53 (13) ◽  
pp. 1240-1246 ◽  
Author(s):  
R. A. Moore
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Structure Constant ◽  
Approximate Solutions ◽  
Order Equation ◽  
Wave Functions ◽  
Fine Structure Constant ◽  
First Order ◽  
Alternative Method ◽  
Electric And Magnetic Fields

An alternative method of obtaining approximate solutions to the Dirac equation is presented. The method takes advantage of the fact that the wave functions can be written as an ordered series in powers of the fine structure constant, α, and that the Hamiltonian can be separated into two parts such that one part connects adjacent orders of the wave function. Energy calculations to order α2, requiring only the solution to the lowest order equation, are considered in this article. The procedure is tested by applying it to the hydrogen atom. It is seen that the lowest order equations are similar to and no more difficult to solve than the nonrelativistic equations for all systems of physical interest. The simplicity and accuracy of the method implies that full relativistic calculations are unnecessary for most situations. The inclusion of electric and magnetic fields and the solution to the first order equation will be considered in later articles.

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