We derive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the extended Floquet
Hilbert space by means of degenerate perturbation theory. The final results are equivalent to those obtained within a different approach [Phys. Rev. A {bf 68}, 013820 (2003), Phys. Rev. X {bf 4}, 031027 (2014)] and can also be related to the Floquet-Magnus expansion [J. Phys. A {bf 34}, 3379 (2000)]. We discuss that the dependence on the driving phase, which plagues the latter, can lead to artifactual symmetry breaking. The high-frequency approach is illustrated using the example of a periodically driven Hubbard model. Moreover, we discuss the nature of the approximation and its limitations for systems of many interacting particles.
