Cauchy Problem and Green's Functions for First Order Differential Operators and Algebraic Quantization
Mathematical Physics
2011-02-28 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
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.
Cite
@article{arxiv.1001.4091,
title = {Cauchy Problem and Green's Functions for First Order Differential Operators and Algebraic Quantization},
author = {Rainer Muehlhoff},
journal= {arXiv preprint arXiv:1001.4091},
year = {2011}
}
Comments
revised version: typos; reordering of sec 2; results unchanged