The classical nonlinear theory of laser-plasma interactions is corrected by taking account of the vacuum polarization effects. A set of wave equations are obtained by using the Heisenberg-Euler Lagrangian density and the derivative correction with the first-order quantum electrodynamic effects. A model more suitable to formulate the interactions of ultra-strong lasers and high-energy-density plasmas is developed. In the result, some environments in which the effects of vacuum polarization will be enhanced are discussed.
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