Geometry and physics of pseudodifferential operators on manifolds

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.

UR - http://www.scopus.com/inward/record.url?scp=84964957512&partnerID=8YFLogxK

U2 - 10.1393/ncc/i2015-15159-1

DO - 10.1393/ncc/i2015-15159-1

M3 - Review

AN - SCOPUS:84964957512

SN - 2037-4909

VL - 38

JO - Nuovo Cimento della Societa Italiana di Fisica C

JF - Nuovo Cimento della Societa Italiana di Fisica C

IS - 5

M1 - 159

ER -