Spectral problems from quantum field theory

Abstract

We describe how spectral functions of differential operators appear in the quantum field theory context. We formulate consistency conditions which should be satisfied by the operators and by the boundary conditions. We review some modern developments in quantum field theory and strings and show which new spectral and boundary value problems arise.

19p., a talk at the Spectral Geometry Workshop, Holbaek, 2003, to be published in Contemporary Mathematics