We study the effects of the quantum vacuum on the propagation of a Gaussian laser beam in vacuum. By means of a double perturbative expansion in paraxiality and quantum vacuum terms, we provide analytical expressions for the self-induced transverse mode mixing, rotation of polarization, and third harmonic generarion. We discuss the possibility of searching for the self-induced, spatially dependent phase shift of a multipetawatt laser pulse, which may allow the testing of quantum electrodynamics and new physics models, such as Born-Infeld theory and models involving new minicharged or axion-like particles, in parametric regions that have not yet been explored in laboratory experiments.
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