Esposito, Giampiero and Napolitano, George M. (2015) Geometry and physics of pseudodifferential operators on manifolds. Il nuovo cimento C, 38 (5). pp. 1-14. ISSN 1826-9885
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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.
| Item Type: | Article |
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| Uncontrolled Keywords: | Partial differential equations; Fourier analysis; Global analysis and analysis on manifolds; Theory of quantized fields |
| Subjects: | 500 Scienze naturali e Matematica > 530 Fisica |
| Depositing User: | Marina Spanti |
| Date Deposited: | 23 Jun 2020 08:54 |
| Last Modified: | 23 Jun 2020 08:54 |
| URI: | http://eprints.bice.rm.cnr.it/id/eprint/19148 |
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