Spectral methods in quantum field theory

Herbert Weigel, Markus Quandt, Noah Graham (auth.)3642001386, 9783642001383

This concise text introduces techniques from quantum mechanics, especially scattering theory, to compute the effects of an external background on a quantum field in general, and on the properties of the quantum vacuum in particular. This approach can be succesfully used in an increasingly large number of situations, ranging from the study of solitons in field theory and cosmology to the determination of Casimir forces in nano-technology.

The method introduced and applied in this book is shown to give an unambiguous connection to perturbation theory, implementing standard renormalization conditions even for non-perturbative backgrounds. It both gives new theoretical insights, for example illuminating longstanding questions regarding Casimir stresses, and also provides an efficient analytic and numerical tool well suited to practical calculations. Last but not least, it elucidates in a concrete context many of the subtleties of quantum field theory, such as divergences, regularization and renormalization, by connecting them to more familiar results in quantum mechanics.

While addressed primarily at young researchers entering the field and nonspecialist researchers with backgrounds in theoretical and mathematical physics, introductory chapters on the theoretical aspects of the method make the book self-contained and thus suitable for advanced graduate students.

Table of contents :
Front Matter….Pages 1-10
Introduction….Pages 1-13
Review of Scattering Theory….Pages 15-32
Quantum Field Theory and the Spectral Method….Pages 33-61
Applications in One Space Dimension….Pages 63-89
Spectral Analysis of Charges….Pages 91-101
Hedgehog Configurations in d = 3+1….Pages 103-128
Boundary Conditions and Casimir Forces….Pages 129-142
String-Type Configurations….Pages 143-169
Quantum Corrections to Q -Balls….Pages 171-177
Back Matter….Pages 1-4