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Spectral Methods in Quantum Field Theory

E-BookPDF1 - PDF WatermarkE-Book
Englisch
Springer Berlin Heidelbergerschienen am05.04.20092009
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.mehr
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Produkt

KlappentextIn 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.
Details
Weitere ISBN/GTIN9783642001390
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format Hinweis1 - PDF Watermark
FormatE107
Erscheinungsjahr2009
Erscheinungsdatum05.04.2009
Auflage2009
ReiheLecture Notes in Physics
Reihen-Nr.777
SpracheEnglisch
IllustrationenXI, 182 p. 30 illus.
Artikel-Nr.8814405
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
Review of Scattering Theory.- Quantum Field Theory and the Spectral Method.- Applications in One Space Dimension.- Spectral Analysis of Charges.- Hedgehog Configurations in = 3+1.- Boundary Conditions and Casimir Forces.- String-Type Configurations.- Quantum Corrections to -Balls.mehr