# Spectral Methods in Quantum Field Theory

Part of the Lecture Notes in Physics book series (LNP, volume 777)

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Part of the Lecture Notes in Physics book series (LNP, volume 777)

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.

calculus casimir forces mathematical physics non-perturbative quantum fluid theory quantum mechanics scattering theory spectral method vaccum energy

- DOI https://doi.org/10.1007/978-3-642-00139-0
- Copyright Information Springer-Verlag Berlin Heidelberg 2009
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Physics and Astronomy
- Print ISBN 978-3-642-00138-3
- Online ISBN 978-3-642-00139-0
- Series Print ISSN 0075-8450
- Series Online ISSN 1616-6361
- Buy this book on publisher's site