Physics – Mathematical Physics
Scientific paper
2011-08-07
Physics
Mathematical Physics
11 pages, no figures
Scientific paper
After introduction of a complex electromagnetic potential, which leaves the electromagnetic fields unchanged, the spinor field can be eliminated from the equations of spinor electrodynamics (the Dirac-Maxwell electrodynamics), and the resulting system of equations for the complex four-potential describes independent evolution of electromagnetic field in the following sense: if components of the complex four-potential and their derivatives with respect to time up to the second order are known at some point in time in the entire 3D space, the equations determine the third-order derivatives of the components with respect to time, so the Cauchy problem can be posed, and the equations can be integrated (at least locally). This result permits mathematical simplification and can be useful for interpretation of quantum theory. A generalized Carleman linearization procedure generates a system of linear equations in the Fock space, which looks like a second-quantized theory and is equivalent to the original nonlinear system on the set of solutions of the latter.
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