by A A Bytsenko (State University of Londrina, Brazil) , G Cognola (University of Trento, Italy) , V Moretti (University of Trento, Italy) , S Zerbini (University of Trento, Italy) , & E Elizalde (IEEE/CSIC & University of Barcelona, Spain)

One of the aims of this book is to explain in a basic manner the seemingly difficult issues of mathematical structure using some specific examples as a guide. In each of the cases considered, a comprehensible physical problem is approached, to which the corresponding mathematical scheme is applied, its usefulness being duly demonstrated. The authors try to fill the gap that always exists between the physics of quantum field theories and the mathematical methods best suited for its formulation, which are increasingly demanding on the mathematical ability of the physicist.

• Survey of Path Integral Quantization and Regularization Techniques
• The Zeta-Function Regularization Method
• Generalized Spectra and Spectral Functions on Non-Commutative Spaces
• Spectral Functions of Laplace Operator on Locally Symmetric Spaces
• Spinor Fields
• Field Fluctuations and Related Variances
• The Multiplicative Anomaly
• Applications of the Multiplicative Anomaly
• The Casimir Effect