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arXiv · 1509.05608

Geometry and physics of pseudodifferential operators on manifolds

Giampiero Esposito·George M. Napolitano
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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: esistence 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.

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Giampiero Esposito, George M. Napolitano. 2016-03-08. Geometry and physics of pseudodifferential operators on manifolds. https://doi.org/10.1393/ncc%2Fi2015-15159-1

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