Geometry and physics of pseudodifferential operators on manifolds
Research output: Contribution to journal › Review › Research › peer-review
Giampiero Esposito, George M. Napolitano
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.
|Journal||Nuovo Cimento della Societa Italiana di Fisica C|
|Publication status||Published - 1 Sep 2015|