Geometry and physics of pseudodifferential operators on manifolds

George Napolitano, Giampiero Esposito

Research output: Contribution to journalArticlepeer-review

Abstract

A review is made of the basic tools used in mathematics to define a
calculus for pseudodifferential operators on Riemannian manifolds endowed with a
connection: existence theorem for the function that generalizes the phase; analogue
of Taylor’s theorem; torsion and curvature terms in the symbolic calculus; the two
kinds of derivative acting on smooth sections of the cotangent bundle of the Riemannian
manifold; the concept of symbol as an equivalence class. Physical motivations
and applications are then outlined, with emphasis on Green functions of quantum
field theory and Parker’s evaluation of Hawking radiation.
Original languageEnglish
Article number159
JournalIl Nuovo Cimento C: colloquia and communications in physics
Volume38
Issue number5
Early online date2016 Mar 31
DOIs
Publication statusPublished - 2016 May 2

Subject classification (UKÄ)

  • Mathematical Analysis

Free keywords

  • Partial differential equations
  • Fourier analysis
  • Global analysis and analysis on manifolds
  • Theory of quantized fields

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