The Dirac Spectrum
Title | The Dirac Spectrum PDF eBook |
Author | Nicolas Ginoux |
Publisher | Springer Science & Business Media |
Pages | 168 |
Release | 2009-06-11 |
Genre | Mathematics |
ISBN | 3642015697 |
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
Title | Dirac Spectra in Dense QCD PDF eBook |
Author | Takuya Kanazawa |
Publisher | Springer Science & Business Media |
Pages | 145 |
Release | 2012-11-02 |
Genre | Science |
ISBN | 4431541659 |
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
Title | Nonlinear Dirac Equation: Spectral Stability of Solitary Waves PDF eBook |
Author | Nabile Boussaïd |
Publisher | American Mathematical Soc. |
Pages | 297 |
Release | 2019-11-21 |
Genre | Education |
ISBN | 1470443953 |
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
Title | Dirac Operators and Spectral Geometry PDF eBook |
Author | Giampiero Esposito |
Publisher | Cambridge University Press |
Pages | 227 |
Release | 1998-08-20 |
Genre | Mathematics |
ISBN | 0521648629 |
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
Title | The Dirac Spectrum on a Cosmic String Loop PDF eBook |
Author | Ralph Lyle |
Publisher | |
Pages | |
Release | 2006 |
Genre | Dirac equation |
ISBN |
Dependence on the Spin Structure of the Dirac Spectrum
Title | Dependence on the Spin Structure of the Dirac Spectrum PDF eBook |
Author | Christian Bär |
Publisher | |
Pages | 16 |
Release | 2000 |
Genre | |
ISBN |
The Dirac Spectrum of Bieberbach Manifolds
Title | The Dirac Spectrum of Bieberbach Manifolds PDF eBook |
Author | Frank Pfäffle |
Publisher | |
Pages | 22 |
Release | 1999 |
Genre | |
ISBN |