Geometry and physics of pseudodifferential operators on manifolds
(2016) In Il Nuovo Cimento C: colloquia and communications in physics 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:
https://lup.lub.lu.se/record/af67b78c-0313-4573-8f15-98ae16d95aad
- author
- Napolitano, George LU and Esposito, Giampiero
- organization
- publishing date
- 2016-05-02
- 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: colloquia and communications in physics
- volume
- 38
- issue
- 5
- article number
- 159
- 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
- 2022-01-30 02:33:32
@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.}},
author = {{Napolitano, George and Esposito, Giampiero}},
issn = {{2037-4909}},
keywords = {{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: colloquia and communications in physics}},
title = {{Geometry and physics of pseudodifferential operators on manifolds}},
url = {{http://dx.doi.org/10.1393/ncc/i2015-15159-1}},
doi = {{10.1393/ncc/i2015-15159-1}},
volume = {{38}},
year = {{2016}},
}