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Andrey alexandrovich bytsenko | centro ciências exatas/uel - Brasil

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In order to investigate quantum effects we shall utilize both methods of noncommutative associative algebra (C* algebra) and K-theory (for field modeís with noncommutative geometry) and spectra! theory - zeta function and heat-kernel methods. For the real hyperbolic manifolds we will consider an expansion in eigenfunctions of the authomorphic Laplacians on the basis of the Selberg trace formula. Thereby, a main difficulty is the calculation of the functional determinants arising in the path integral. We shall use the elements of spectral theory of (pseudo) differential operators, differential geometry, theory of characteristic classes and cohomology. Such approach enables one to derive loop expansions in the presence of nontrivial topology. The main goals of thís project are: Evaluation of the partition function (topological invariants) associated with locally symmetric spaces of rank one; calculation of the global anomalies. (AU)

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