Geometry and physics of pseudodifferential operators on manifolds

Publikation: Bidrag til tidsskriftReviewForskningfagfællebedømt


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.

TidsskriftNuovo Cimento della Societa Italiana di Fisica C
Udgave nummer5
Antal sider14
StatusUdgivet - 1 sep. 2015
Eksternt udgivetJa

ID: 194769539