6533b7dcfe1ef96bd1272179
RESEARCH PRODUCT
On global solutions of the Maxwell-Dirac equations
Jacques SimonMoshé FlatoErik Taflinsubject
Momentum operatorElectromagnetic wave equationMathematical analysisStatistical and Nonlinear PhysicsInhomogeneous electromagnetic wave equationd'Alembert's formula35Q20Operator (computer programming)35L45Initial value problemD'Alembert operatorHyperbolic partial differential equation35P25Mathematical Physics81D25Mathematicsdescription
We prove, for the Maxwell-Dirac equations in 1+3 dimensions, that modified wave operators exist on a domain of small entire test functions of exponential type and that the Cauchy problem, inR+×R3, has a unique solution for each initial condition (att=0) which is in the image of the wave operator. The modification of the wave operator, which eliminates infrared divergences, is given by approximate solutions of the Hamilton-Jacobi equation, for a relativistic electron in an electromagnetic potential. The modified wave operator linearizes the Maxwell-Dirac equations to their linear part.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1987-03-01 | Communications in Mathematical Physics |