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Spectral Methods in Quantum Field Theory

2009-05-08 Science
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Release : 2009-05-08
Genre : Science
Kind : eBook
Book Rating : 386/5 ( reviews)

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Book Synopsis Spectral Methods in Quantum Field Theory by : Noah Graham

Download or read book Spectral Methods in Quantum Field Theory written by Noah Graham. This book was released on 2009-05-08. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph we apply scattering theory methods to calculations in quantum ?eld theory, with a particular focus on properties of the quantum vacuum. These methods will provide e?cient and reliable solutions to a - riety of problems in quantum ?eld theory. Our approach will also elucidate in a concrete context many of the subtleties of quantum ?eld theory, such as divergences, regularization, and renormalization, by connecting them to more familiar results in quantum mechanics. We will use tools of scattering theory to characterize the spectrum of energyeigenstatesinapotentialbackground,hencethetermspectralmethods. This mode spectrum comprises both discrete bound states and a continuum of scattering states. We develop a powerful formalism that parameterizes the e?ects of the continuum by the density of states, which we compute from scattering data. Summing the zero-point energies of these modes gives the energy of the quantum vacuum, which is one of the central quantities we study.Althoughthemostcommonlystudiedbackgroundpotentialsarisefrom static soliton solutions to the classical equations of motion, these methods are not limited to such cases.

Spectral Methods in Quantum Field Theory and the Center Vortex Model

2006
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Release : 2006
Genre :
Kind : eBook
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Book Synopsis Spectral Methods in Quantum Field Theory and the Center Vortex Model by : Markus Quandt

Download or read book Spectral Methods in Quantum Field Theory and the Center Vortex Model written by Markus Quandt. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt:

Operators, Geometry and Quanta

2011-06-25 Science
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Release : 2011-06-25
Genre : Science
Kind : eBook
Book Rating : 051/5 ( reviews)

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Book Synopsis Operators, Geometry and Quanta by : Dmitri Fursaev

Download or read book Operators, Geometry and Quanta written by Dmitri Fursaev. This book was released on 2011-06-25. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.

Spectral methods in infinite-dimensional analysis. 2 (1995)

1995 Degree of freedom
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Release : 1995
Genre : Degree of freedom
Kind : eBook
Book Rating : 483/5 ( reviews)

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Book Synopsis Spectral methods in infinite-dimensional analysis. 2 (1995) by : I︠U︡riĭ Makarovich Berezanskiĭ

Download or read book Spectral methods in infinite-dimensional analysis. 2 (1995) written by I︠U︡riĭ Makarovich Berezanskiĭ. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt:

Spectral Methods and Their Applications

1998 Mathematics
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Release : 1998
Genre : Mathematics
Kind : eBook
Book Rating : 334/5 ( reviews)

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Book Synopsis Spectral Methods and Their Applications by : Benyu Guo

Download or read book Spectral Methods and Their Applications written by Benyu Guo. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic algorithms, the main theoretical results, and some applications of spectral methods. Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other fields.The book consists of three parts. The first part deals with orthogonal approximations in Sobolev spaces and the stability and convergence of approximations for nonlinear problems, as the mathematical foundation of spectral methods. In the second part, various spectral methods are described, with some applications. It includes Fourier spectral method, Legendre spectral method, Chebyshev spectral method, spectral penalty method, spectral vanishing viscosity method, spectral approximation of isolated solutions, multi-dimensional spectral method, spectral method for high-order equations, spectral-domain decomposition method and spectral multigrid method. The third part is devoted to some recent developments of spectral methods, such as mixed spectral methods, combined spectral methods and spectral methods on the surface.

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