Asymptotic Completeness, Global Existence and the Infrared Problem for the Maxwell-Dirac Equations.

Flato, Moshé:

ISBN 10: 0821806831 / ISBN 13: 9780821806838

Editore: Providence, American Mathematical Society, 1997

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311 S. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. Ex-library in GOOD condition with library-signature and stamp(s). Some traces of use. R-16116 9780821806838 Sprache: Englisch Gewicht in Gramm: 550. Codice articolo 2479578

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Titolo: Asymptotic Completeness, Global Existence ...

Casa editrice: Providence, American Mathematical Society

Data di pubblicazione: 1997

Legatura: Softcover

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Riassunto:

The purpose of this work is to present and give full proofs of new original research results concerning integration of and scattering for the classical Maxwell-Dirac equations. These equations govern first quantized electrodynamics and are the starting point for a rigorous formulation of quantum electrodynamics. The presentation is given within the formalism of nonlinear group and Lie algebra representations, i.e. the powerful new approach to nonlinear evolution equations covariant under a group action.The authors prove that the nonlinear Lie algebra representation given by the manifestly covariant Maxwell-Dirac equations is integrable to a global nonlinear representation of the Poincare group on a differentiable manifold of small initial conditions. This solves, in particular, the small-data Cauchy problem for the Maxwell-Dirac equations globally in time. The existence of modified wave operators and asymptotic completeness is proved. The asymptotic representations (at infinite time) turn out to be nonlinear. A cohomological interpretation of the results in the spirit of nonlinear representation theory and its connection to the infrared tail of the electron are developed.