Partial differential equations and quantum states in curved spacetimes

Zhirayr Avetisyan*, Matteo Capoferri

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

2 Citations (Scopus)
74 Downloads (Pure)


In this review paper, we discuss the relation between recent advances in the theory of partial differential equations and their applications to quantum field theory on curved spacetimes. In particular, we focus on hyperbolic propagators and the role they play in the construction of physically admissible quantum states—the so-called Hadamard states—on globally hyperbolic spacetimes. We will review the notion of a propagator and discuss how it can be constructed in an explicit and invariant fashion, first on a Riemannian manifold and then on a Lorentzian spacetime. Finally, we will recall the notion of Hadamard state and relate the latter to hyperbolic propagators via the wavefront set, a subset of the cotangent bundle capturing the information about the singularities of a distribution.

Original languageEnglish
Article number1936
Issue number16
Publication statusPublished - 13 Aug 2021


  • Hadamard states
  • Hyperbolic propagators
  • Partial differential equations
  • Quantum field theory

ASJC Scopus subject areas

  • General Mathematics


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