Nonlinear Dirac Equation

Author : Nabile Boussaïd
Publisher : American Mathematical Soc.
ISBN 13 : 1470443953
Total Pages : 297 pages
Book Rating : 4.55/5 ( download)

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Download or read book Nonlinear Dirac Equation: Spectral Stability of Solitary Waves written by Nabile Boussaïd and published by American Mathematical Soc.. This book was released on 2019-11-21 with total page 297 pages. 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.

Author : Nabile Boussaïd
Publisher :
ISBN 13 : 9781470454227
Total Pages : 297 pages
Book Rating : 4.2X/5 ( download)

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Download or read book Nonlinear Dirac Equation written by Nabile Boussaïd and published by . This book was released on 1920 with total page 297 pages. 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

Author : Claude Daviau
Publisher :
ISBN 13 : 9781907343582
Total Pages : 0 pages
Book Rating : 4.8X/5 ( download)

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Download or read book Nonlinear Dirac Equation, Magnetic Monopoles and Double Space-time written by Claude Daviau and published by . This book was released on 2012 with total page 0 pages. 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.

Author : Victoriano Carmona
Publisher : Springer
ISBN 13 : 3319667661
Total Pages : 424 pages
Book Rating : 4.69/5 ( download)

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Download or read book Nonlinear Systems, Vol. 1 written by Victoriano Carmona and published by Springer. This book was released on 2018-09-15 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.81/5 ( download)

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Download or read book Solitary Waves in Nonlinear Dirac Equation written by and published by . This book was released on 2015 with total page pages. 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.

Author : Alexander G. Kyriakos
Publisher : AKVY PRESS
ISBN 13 : 0980966744
Total Pages : 164 pages
Book Rating : 4.49/5 ( download)

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Download or read book The Nonlinear Quantum Field Theory as a Generalization of Standard Model (geometrical Approach) written by Alexander G. Kyriakos and published by AKVY PRESS. This book was released on 2009 with total page 164 pages. 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.

Author : Yaser Hasan Muhmad Sabbah
Publisher :
ISBN 13 :
Total Pages : 172 pages
Book Rating : 4.82/5 ( download)

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Download or read book Exact Localized Solutions of the Nonlinear Dirac Equation written by Yaser Hasan Muhmad Sabbah and published by . This book was released on 2017 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Graham Farmelo
Publisher : Faber & Faber
ISBN 13 : 0571250076
Total Pages : 554 pages
Book Rating : 4.73/5 ( download)

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Download or read book The Strangest Man written by Graham Farmelo and published by Faber & Faber. This book was released on 2009-01-22 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'A monumental achievement - one of the great scientific biographies.' Michael Frayn The Strangest Man is the Costa Biography Award-winning account of Paul Dirac, the famous physicist sometimes called the British Einstein. He was one of the leading pioneers of the greatest revolution in twentieth-century science: quantum mechanics. The youngest theoretician ever to win the Nobel Prize for Physics, he was also pathologically reticent, strangely literal-minded and legendarily unable to communicate or empathize. Through his greatest period of productivity, his postcards home contained only remarks about the weather.Based on a previously undiscovered archive of family papers, Graham Farmelo celebrates Dirac's massive scientific achievement while drawing a compassionate portrait of his life and work. Farmelo shows a man who, while hopelessly socially inept, could manage to love and sustain close friendship.The Strangest Man is an extraordinary and moving human story, as well as a study of one of the most exciting times in scientific history. 'A wonderful book . . . Moving, sometimes comic, sometimes infinitely sad, and goes to the roots of what we mean by truth in science.' Lord Waldegrave, Daily Telegraph

Author : Laith H. Haddad
Publisher :
ISBN 13 :
Total Pages : 353 pages
Book Rating : 4.67/5 ( download)

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Download or read book Nonlinear Dirac Equation in Bose-Einstein Condensates written by Laith H. Haddad and published by . This book was released on 2012 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Pierre Deligne
Publisher : American Mathematical Society
ISBN 13 : 0821820133
Total Pages : 801 pages
Book Rating : 4.31/5 ( download)

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Download or read book Quantum Fields and Strings: A Course for Mathematicians written by Pierre Deligne and published by American Mathematical Society. This book was released on 1999-10-25 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.