登入選單
返回Google圖書搜尋
Asymptotic Completeness, Global Existence and the Infrared Problem for the Maxwell-Dirac Equations
Moshé FlatoJacques Charles Henri SimonErik Taflin
出版American Mathematical Soc., 1997
主題Mathematics / Differential Equations / GeneralScience / Physics / ElectricityScience / Physics / ElectromagnetismScience / Physics / Quantum Theory
ISBN08218068319780821806838
URLhttp://books.google.com.hk/books?id=54fTCQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.