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Nonlinear Dirac Equation: Spectral Stability of Solitary Waves

2019-11-21 Education
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Release : 2019-11-21
Genre : Education
Kind : eBook
Book Rating : 953/5 ( reviews)

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Book Synopsis Nonlinear Dirac Equation: Spectral Stability of Solitary Waves by : Nabile Boussaïd

Download or read book Nonlinear Dirac Equation: Spectral Stability of Solitary Waves written by Nabile Boussaïd. This book was released on 2019-11-21. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.

Nonlinear Dirac Equation

1920 Differential equations, Partial
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Author :
Release : 1920
Genre : Differential equations, Partial
Kind : eBook
Book Rating : 227/5 ( reviews)

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Book Synopsis Nonlinear Dirac Equation by : Nabile Boussaïd

Download or read book Nonlinear Dirac Equation written by Nabile Boussaïd. This book was released on 1920. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation

Nonlinear Dirac Equation, Magnetic Monopoles and Double Space-time

2012 Mathematics
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Release : 2012
Genre : Mathematics
Kind : eBook
Book Rating : 582/5 ( reviews)

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Book Synopsis Nonlinear Dirac Equation, Magnetic Monopoles and Double Space-time by : Claude Daviau

Download or read book Nonlinear Dirac Equation, Magnetic Monopoles and Double Space-time written by Claude Daviau. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: Beginnings of quantum mechanics are revised and the author starts from the point where relativity and quantum mechanics were compatible. A modified wave equation for the electron is used. The relativistic invariance is then enlarged to a greater invariance group and the first consequences are studied. This invariance applies to the whole electromagnetism, including magnetic monopoles. Another space-time variety is seen which is very different from the usual relativistic space-time.

Solitary Waves in Nonlinear Dirac Equation

2015
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Release : 2015
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Solitary Waves in Nonlinear Dirac Equation by :

Download or read book Solitary Waves in Nonlinear Dirac Equation written by . This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt: This report describes the implementation of nonlinear Dirac equations in the calculation of solitary waves. Conclusions and comments on quantum elasticity are also included.

The Nonlinear Quantum Field Theory as a Generalization of Standard Model (geometrical Approach)

2009 Quantum field theory
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Release : 2009
Genre : Quantum field theory
Kind : eBook
Book Rating : 744/5 ( reviews)

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Book Synopsis The Nonlinear Quantum Field Theory as a Generalization of Standard Model (geometrical Approach) by : Alexander G. Kyriakos

Download or read book The Nonlinear Quantum Field Theory as a Generalization of Standard Model (geometrical Approach) written by Alexander G. Kyriakos. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: The author proposes a special nonlinear quantum field theory. In a linear approximation, this theory can be presented in the form of the Standard Model (SM) theory. The richer physical structure of this nonlinear theory makes it possible to exceed the limits of SM and remove its known incompleteness. We show that nonlinearity of the field is critical for the appearance of charges and masses of elementary particles, for confinement of quarks, and many other effects, whose description within the framework of SM causes difficulties. In this case, the mechanism of generation of masses is mathematically similar to Higgs's mechanism, but it is considerably simpler and does not include the additional particles. The proposed theory does not examine the theory of gravity, but reveals the mathematical similarity of the nonlinear field equations of both theories. The book is intended for undergraduate and graduate students studying the theory of elementary particles, as well as for specialists working in this field.

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