On the positivity of propagator differences
Andr\'as Vasy
TL;DR
This paper explores the positivity characteristics of distinguished propagators, which are special inverses of operators in scattering and wave theory, connecting to foundational work in quantum field theory on curved spacetimes.
Contribution
It establishes a link between positivity properties of propagators and the theory of distinguished parametrices, advancing understanding in mathematical physics.
Findings
Positivity properties of distinguished propagators are characterized.
Connections to Duistermaat and Hörmander's work on parametrices are clarified.
Implications for quantum field theory on curved spacetimes are discussed.
Abstract
We discuss positivity properties of `distinguished propagators', i.e. distinguished inverses of operators that frequently occur in scattering theory and wave propagation. We relate this to the work of Duistermaat and H\"ormander on distinguished parametrices (approximate inverses), which has played a major role in quantum field theory on curved spacetimes recently.
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