Operators, Geometry and Quanta: Methods of Spectral Geometry in Quantum Field Theory (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). More than hundred exercises together with their solutions are included. This book addresses advanced graduate students and researchers in mathematical physics and in neighbouring areas 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. Biocontrol is among the most promising methods for a safe, environmentally benign and sustainable crop protection. Microbial pesticides offer a great potential, and it is anticipated that they will become a substantial part of the use of all crop protection products. Their development and commercialization, however, has been difficult and with many failures. For the first time, a rational and structured roadmap has been designed for the development and commercialization of microbial pest control products, based on entomopathogenic bacteria, fungi, viruses and nematodes, for the control of arthropod pests. The emphasis lies on strain screening, product development, up to successful commercialization, from a bio-industry's viewpoint. The building blocks of the entire process are identified. The selection criteria for a microbial pest control agent are defined as well as critical parameters for the development of the product. Implementation of the product into an integrated pest management programme is pivotal for a substantial market uptake. Three phases are distinguished for successful adoption in the market: an appropriate application strategy, an optimal implementation strategy, and an effective adoption strategy. Key success and failure factors are identified. Registration is a major hurdle for biopesticides. Salient registration issues are treated and useful information presented. The road to a successful microbial pest control product is designed. Diagrams illustrate the stepwise approach of the entire process. A future perspective on the biopesticide market is presented with limiting and promotional factors and trends. The significant drivers for success are food safety concern, new research and technology, changes in the regulatory climate, and the occurrence of new invasive pests. This systematic roadmap with a strong focus on economics and market introduction will assist academic researchers and industrial developers of biopesticides in accomplishing their goal: the development of successful cost-effective microbial pesticides Front Matter....Pages I-XVI Front Matter....Pages 1-1 Geometrical Background....Pages 3-28 Quantum Fields....Pages 29-50 Front Matter....Pages 51-51 Operators and Their Spectra....Pages 53-65 Heat Equation....Pages 67-94 Spectral Functions....Pages 95-114 Non-linear Spectral Problems....Pages 115-124 Front Matter....Pages 125-125 Effective Action....Pages 127-155 Quantum Anomalies....Pages 157-176 Vacuum Energy....Pages 177-196 Open Strings and Born-Infeld Action....Pages 197-204 Noncommutative Geometry and Field Theory....Pages 205-217 Front Matter....Pages 219-219 Solutions to Exercises....Pages 221-271 Back Matter....Pages 273-286