  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.
