Asymptotic Completeness, Global Existence and the Infrared Problem for the Maxwell-Dirac Equations (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Flato, M.; Simon, Jacques C. H.; Taflin, Erik

Softcover

ISBN 10: 0821806831 ISBN 13: 9780821806838

Publisher: American Mathematical Society, 1997

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1997
• Language: English
• ISBN 10: 0821806831
• ISBN 13: 9780821806838
• Binding: Paperback
• Edition number: 1
• Number of pages: 311