Global and microlocal aspects of Dirac operators: propagators and Hadamard states

Matteo Capoferri; Simone Murro

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arXiv · 2201.12104

Global and microlocal aspects of Dirac operators: propagators and Hadamard states

Matteo Capoferri·Simone Murro

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Abstract

We propose a geometric approach to construct the Cauchy evolution operator for the Lorentzian Dirac operator on Cauchy-compact globally hyperbolic 4-manifolds. We realise the Cauchy evolution operator as the sum of two invariantly defined oscillatory integrals -- the positive and negative Dirac propagators -- global in space and in time, with distinguished complex-valued geometric phase functions. As applications, we relate the Cauchy evolution operators with the Feynman propagator and construct Cauchy surfaces covariances of quasifree Hadamard states.

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Matteo Capoferri, Simone Murro. 2022-01-28. Global and microlocal aspects of Dirac operators: propagators and Hadamard states. https://arxiv.org/abs/2201.12104

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