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Analysis Seminar
Nonrelativistic/Classical Limits for the Dirac Maxwell system
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We study the behavior of solutions of the (mixed state) Dirac-Maxwell system in the (simultaneous) non-relativistic and semi-classical limits, i.e., as the speed of light tends to infinity and the Planck constant tends to zero. Under suitable assumptions and under conditions on the initial data, we prove that the scalar Wigner transform of the Dirac spinors converges weakly to a solution of the classical Vlasov-Poisson system. Our key technique is a blend of null form bilinear estimates a la Klainerman-Machedon with the machinery of the Wigner transform. |