Cel
The aim of the project is to use the scientific collaboration between the Russian, Italian and German researchers in solution of the following problems:
- To study the dynamical properties of quantum systems by using methods of noncommutative probability, infinite dimensional analysis, differential geometry and p-adic analysis;
- In particular to investigate the mathematical and also applied aspects of the new approach to renormalized quantum stochastic calculus based on white noise and theory of generalized functions, to determine the higher order corrections to the stochastic limit for various models in quantum field theory, to develop the theory of representations of interacting commutation relations, to develop a new approach to deformation quantization based on white noise analysis, to generalise the loop space formulation of gauge theories to the noncommutative case, to investigate p-adic stochastic processes and its applications to models of relaxation in spin glasses and other disordered systems;
- To investigate connections between quantum stochastic differential equations and boundary value problems in Hilbert Fock module. To study criteria for a boundary value problem in Hilbert Fock module to be symmetric and selfadjoint;
- To develop functional integration and Monte-Carlo methods to boundary value problems related to quantum optics and detection of gravitational waves.
The variety of used methods and results shows the interdisciplinary character of the project. The main emphasise will be on noncommutative (quantum) probability. The obtained results will have significant mathematical value as well as the importance for applications.
Results of this project will be presented at conferences and schools on noncommutative probability, mathematical physics, quantum field theory and statistical physics, published in papers and books.
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00133 Rome
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