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.
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.
Original language | English |
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Article number | 159 |
Journal | Il Nuovo Cimento C: colloquia and communications in physics |
Volume | 38 |
Issue number | 5 |
Early online date | 2016 Mar 31 |
DOIs | |
Publication status | Published - 2016 May 2 |
Subject classification (UKÄ)
- Mathematical Analysis
Free keywords
- Partial differential equations
- Fourier analysis
- Global analysis and analysis on manifolds
- Theory of quantized fields