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.
Original languageEnglish
JournalAdvances in Differential Equations
Publication statusAccepted/In press - 14 Sept 2023

Keywords

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

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