Cauchy Problem and Green's Functions for First Order Differential Operators and Algebraic Quantization

Abstract

Existence and uniqueness of advanced and retarded fundamental solutions (Green's functions) and of global solutions to the Cauchy problem is proved for a general class of first order linear differential operators on vector bundles over globally hyperbolic Lorentzian manifolds. This is a core ingredient to CAR-/CCR-algebraic constructions of quantum field theories on curved spacetimes, particularly for higher spin field equations.Comment: revised version: typos; reordering of sec 2; results unchange