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Geometry and physics of pseudodifferential operators on manifolds

Napolitano, George LU and Esposito, Giampiero (2016) In Il Nuovo Cimento C 38(5).
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.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Partial differential equations, Fourier analysis, Global analysis and analysis on manifolds, Theory of quantized fields
in
Il Nuovo Cimento C
volume
38
issue
5
publisher
Società italiana di fisica
external identifiers
  • WOS:000374847700005
  • Scopus:84964957512
ISSN
2037-4909
DOI
10.1393/ncc/i2015-15159-1
language
English
LU publication?
yes
id
af67b78c-0313-4573-8f15-98ae16d95aad
date added to LUP
2016-04-11 12:41:25
date last changed
2017-01-01 08:22:16
@article{af67b78c-0313-4573-8f15-98ae16d95aad,
  abstract     = {A review is made of the basic tools used in mathematics to define a<br/>calculus for pseudodifferential operators on Riemannian manifolds endowed with a<br/>connection: existence theorem for the function that generalizes the phase; analogue<br/>of Taylor’s theorem; torsion and curvature terms in the symbolic calculus; the two<br/>kinds of derivative acting on smooth sections of the cotangent bundle of the Riemannian<br/>manifold; the concept of symbol as an equivalence class. Physical motivations<br/>and applications are then outlined, with emphasis on Green functions of quantum<br/>field theory and Parker’s evaluation of Hawking radiation.},
  articleno    = {159},
  author       = {Napolitano, George and Esposito, Giampiero},
  issn         = {2037-4909},
  keyword      = {Partial differential equations,Fourier analysis,Global analysis and analysis on manifolds,Theory of quantized fields},
  language     = {eng},
  month        = {05},
  number       = {5},
  publisher    = {Società italiana di fisica},
  series       = {Il Nuovo Cimento C},
  title        = {Geometry and physics of pseudodifferential operators on manifolds},
  url          = {http://dx.doi.org/10.1393/ncc/i2015-15159-1},
  volume       = {38},
  year         = {2016},
}