Operators, Geometry and Quanta

Methods of Spectral Geometry in Quantum Field Theory
2011
ISBN: 978-94-007-0204-2
Verlag: Springer Netherlands

Buch, Englisch, 288 Seiten, HC gerader Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 623 g

Reihe: Theoretical and Mathematical Physics

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.

Zielgruppe

Research

Autoren/Hrsg.

Vassilevich, Dmitri

Fursaev, Dmitri

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Geometrie Geometrie der modernen Physik

Inhaltsverzeichnis

1 Preface.- 2 Notation Index I The Basics: 3 Geometrical Background.- 4 Quantum fields II Spectral geometry: 5 Operators and their spectra.- 6 Spectral functions.- 7 Non-linear spectral problems.- 8 Anomalies and Index Theorem III Applications: 9 Effective action.- 10 Anomalies in quantum field theories.- 11 Vacuum energy.- 12 Open strings and Born-Infeld action.- 13 Noncommutative geometry and field theory IV Problem solving: 14 Solutions to exercises.

Über Autor(innen)

The authors D. Vassilevich and D. Fursaev are acknowledged experts in spectral geometry and quantum gravity. D. Fursaev has published more than 60 articles in high profile science journals, and he was appointed the rector of Dubna International University in 2008. D. Vassilevich is a professor for mathematical physics at the Universidade Federal do ABC, Santo Andre (Brazil). He published more than 100 articles in scientific journals and is author of the book "”Fundamental Interactions - A Memorial Volume for Wolfgang Kummer" (2009).