Trace and determinant functionals on operator algebras provide a means of constructing invariants in analysis, topology, differential geometry, analytic number theory, and quantum field theory. The consequent developments around such invariants have led to significant advances both in pure mathematics and theoretical physics. As the fundamental tools of trace theory have become well understood and clear general structures have emerged, so the need for specialist
texts which explain the basic theoretical principles and computational techniques has become increasingly urgent.
Providing a broad account of the theory of traces and determinants on algebras of differential and pseudodifferential operators over compact manifolds, this text is the first to deal with trace theory in general, encompassing a number of the principle applications and backed up by specific computations which set out in detail the nuts-and-bolts of the basic theory. Both the microanalytic approach to traces and determinants via pseudodifferential operator theory and the more computational
approach directed by applications in geometric analysis, are developed in a general framework that will be of interest to mathematicians and physicists in a number of different fields.
Dr. Scott obtained his D.Phil. from Oxford University in 1992. He went on to hold post doctoral positions in Oxford University, the Universidad de los Andes in Bogota, and then for two years at the research institute `SISSA' in Trieste, Italy. In 1998 he was appointed to the mathematics department at King's College London.
Introduction ; 1. Traces ; 2. Determinants ; 3. Computations, transition formulae, and the local index formula ; 4. Pseudodifferential operator trace formulae ; 5. Geometric families of pseudodifferential operators and determinant line bundles ; List of symbols ; References ; Index