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.

revised version: typos; reordering of sec 2; results unchanged

References in corpus (1)

• The locally covariant Dirac field

Cited by in corpus (7)

• Classical and Quantum Fields on Lorentzian Manifolds
• Linear bosonic and fermionic quantum gauge theories on curved spacetimes
• The renormalized locally covariant Dirac field
• Hadamard states for quantized Dirac fields on Lorentzian manifolds of bounded geometry
• Pure quasifree states of the Dirac field from the fermionic projector
• Quantum field theory in static external potentials and Hadamard states
• Hadamard property of the in and out states for Dirac fields on asymptotically static spacetimes