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

Matteo Capoferri, Simone Murro

Research output: Working paperPreprint

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.
Original languageEnglish
DOIs
Publication statusPublished - 28 Jan 2022

Keywords

  • math.AP
  • math-ph
  • math.DG
  • math.MP
  • Primary 35L45, 35Q41, 58J40, Secondary 53C50, 58J45, 81T05

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