Geometry and physics of pseudodifferential operators on manifolds

• A review is made of the basic tools used in mathematics to define acalculus for pseudodifferential operators on Riemannian manifolds endowed with aconnection: existence theorem for the function that generalizes the phase; analogueof Taylor’s theorem; torsion and curvature terms in the symbolic calculus; the twokinds of derivative acting on smooth sections of the cotangent bundle of the Riemannianmanifold; the concept of symbol as an equivalence class. Physical motivationsand applications are then outlined, with emphasis on Green functions of quantumfield theory and Parker’s evaluation of Hawking radiation.

Ämnesord

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Partial differential equations

Fourier analysis

Global analysis and analysis on manifolds

Theory of quantized fields

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art (ämneskategori)

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