Overview

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.

Full Product Details

Author:   Noah Graham ,  Markus Quandt ,  Herbert Weigel
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2009 ed.
Volume:   777
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   0.465kg
ISBN:  

9783642001383

ISBN 10:   3642001386
Pages:   182
Publication Date:   08 May 2009
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

Reviews

From the reviews: The authors present the mathematics that is foundational to a variety of problems in quantum field theory, in particular the subtleties of calculating the zero-point energy, i.e. the energy of the vacuum. ! This monograph ! should be used by graduate students as a companion to the standard textbooks of QFT. (Gert Roepstorff, Zentralblatt MATH, Vol. 1169, 2009)

From the reviews: The authors present the mathematics that is foundational to a variety of problems in quantum field theory, in particular the subtleties of calculating the zero-point energy, i.e. the energy of the vacuum. ... This monograph ... should be used by graduate students as a companion to the standard textbooks of QFT. (Gert Roepstorff, Zentralblatt MATH, Vol. 1169, 2009)

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