Geometry and physics of pseudodifferential operators on manifolds
Publikation: Bidrag til tidsskrift › Review › fagfællebedømt
Standard
Geometry and physics of pseudodifferential operators on manifolds. / Esposito, Giampiero; Napolitano, George M.
I: Nuovo Cimento della Societa Italiana di Fisica C, Bind 38, Nr. 5, 159, 01.09.2015.Publikation: Bidrag til tidsskrift › Review › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Geometry and physics of pseudodifferential operators on manifolds
AU - Esposito, Giampiero
AU - Napolitano, George M.
PY - 2015/9/1
Y1 - 2015/9/1
N2 - 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.
AB - 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.
U2 - 10.1393/ncc/i2015-15159-1
DO - 10.1393/ncc/i2015-15159-1
M3 - Review
AN - SCOPUS:84964957512
VL - 38
JO - Nuovo Cimento della Societa Italiana di Fisica C
JF - Nuovo Cimento della Societa Italiana di Fisica C
SN - 2037-4909
IS - 5
M1 - 159
ER -
ID: 194769539