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The Dirac Spectrum

2009-06-11 Mathematics
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Release : 2009-06-11
Genre : Mathematics
Kind : eBook
Book Rating : 697/5 ( reviews)

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Book Synopsis The Dirac Spectrum by : Nicolas Ginoux

Download or read book The Dirac Spectrum written by Nicolas Ginoux. This book was released on 2009-06-11. Available in PDF, EPUB and Kindle. Book excerpt: This volume surveys the spectral properties of the spin Dirac operator. After a brief introduction to spin geometry, we present the main known estimates for Dirac eigenvalues on compact manifolds with or without boundaries. We give examples where the spectrum can be made explicit and present a chapter dealing with the non-compact setting. The methods mostly involve elementary analytical techniques and are therefore accessible for Master students entering the subject. A complete and updated list of references is also included.

Dirac Spectra in Dense QCD

2012-11-02 Science
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Release : 2012-11-02
Genre : Science
Kind : eBook
Book Rating : 659/5 ( reviews)

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Book Synopsis Dirac Spectra in Dense QCD by : Takuya Kanazawa

Download or read book Dirac Spectra in Dense QCD written by Takuya Kanazawa. This book was released on 2012-11-02. Available in PDF, EPUB and Kindle. Book excerpt: Gaining a theoretical understanding of the properties of ultra-relativistic dense matter has been one of the most important and challenging goals in quantum chromodynamics (QCD). In this thesis, the author analyzes dense quark matter in QCD with gauge group SU(2) using low-energy effective theoretical techniques and elucidates a novel connection between statistical properties of the Dirac operator spectrum at high baryon chemical potential and a special class of random matrix theories. This work can be viewed as an extension of a similar correspondence between QCD and matrix models which was previously known only for infinitesimal chemical potentials. In future numerical simulations of dense matter the analytical results reported here are expected to serve as a useful tool to extract physical observables such as the BCS gap from numerical data on the Dirac spectrum.

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.

Dirac Operators and Spectral Geometry

1998-08-20 Mathematics
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Release : 1998-08-20
Genre : Mathematics
Kind : eBook
Book Rating : 629/5 ( reviews)

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Book Synopsis Dirac Operators and Spectral Geometry by : Giampiero Esposito

Download or read book Dirac Operators and Spectral Geometry written by Giampiero Esposito. This book was released on 1998-08-20. Available in PDF, EPUB and Kindle. Book excerpt: A clear, concise and up-to-date introduction to the theory of the Dirac operator and its wide range of applications in theoretical physics for graduate students and researchers.

The Dirac Spectrum on a Cosmic String Loop

2006 Dirac equation
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Release : 2006
Genre : Dirac equation
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis The Dirac Spectrum on a Cosmic String Loop by : Ralph Lyle

Download or read book The Dirac Spectrum on a Cosmic String Loop written by Ralph Lyle. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt:

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