Quantum vacuum nonlinearities in strong electromagnetic fields

The physical vacuum of a relativistic quantum field theory amounts to a non-trivial quantum state. It encodes information about the full particle content of the underlying microscopic theory in the form of virtual processes, also referred to as vacuum fluctuations. If the theory features charged particles, fluctuations of the latter give rise to nonlinear effective couplings between electromagnetic fields that vanish in the formal limit of a vanishing Planck constant, but persist for a nonzero physical value. In turn, they inherently modify Maxwell’s linear theory of classical electrodynamics. However, for the field strengths reached by macroscopic electromagnetic fields currently available in the laboratory the quantum vacuum nonlinearities induced by Standard Model particles are parametrically suppressed relatively to the linear contribution by inverse powers of the electron mass and thus very small. As a consequence, this fundamental tenet has remained experimentally challenging and is yet to be tested in the laboratory. The present work is devoted to the study of quantum vacuum nonlinearities in strong electromagnetic fields arising from quantum electrodynamics. It provides a detailed account of the state of the art of analytical theory. On the one hand, it focuses on fundamental theoretical aspects concerning the structure and behavior of the Heisenberg-Euler effective action, which supersedes the classical Maxwell action in governing the physics of strong macroscopic electromagnetic fields in the quantum vacuum. On the other hand, it is concerned with questions of direct phenomenological relevance like the systematic study of photonic quantum vacuum signals accessible with state-of-the-art laser technology.