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arXiv · 1001.4091

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

Rainer Muehlhoff
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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.

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Rainer Muehlhoff. 2011-02-21. Cauchy Problem and Green's Functions for First Order Differential Operators and Algebraic Quantization. https://doi.org/10.1063/1.3530846

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