Zeta invariants in geometry and physics

• Grant number: 07/07141-8
• Support Opportunities: Scholarships abroad - Research
• Start date: January 06, 2008
• End date: June 05, 2008
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Mauro Spreafico
• Grantee: Mauro Spreafico
• Host Investigator: Sergio Zerbini
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universitá degli Studi di Trento, Italy

Abstract

The aim of this project is to continue the investigation on the zeta functions of the $S$-sequences started in my recent works (ref. 26, 27, 28), and to apply the techniques developed to the following three types of problems: relative zeta determinants and perturbation determinants, analytic torsion, relative zeta determinants and spectral analysis on non compact spaces. In particular, in the preprint 'Relative spectral functions for two point interaction in three dimensions' (ref. 30), with S. Zerbini (Trento), we face the problem of the construction of a geometric model for a quantum filed theory at finite temperature on a non compact domain using zeta regularization techniques. This can be done using results of W. Muller on relative zeta determinants. Beside the particular result for a two point’s interaction, our aim is too built up a general theory and applies it to other models. (AU)