  We examine the low-energy physics of graphene in the presence of a circularly
polarized electric field in the terahertz regime. Specifically, we derive a
general expression for the dynamical polarizability of graphene irradiated by
an ac electric field. Several approximations are developed that allow one to
develop a semianalytical theory for the weak field regime. The ac field changes
qualitatively the single and many electron excitations of graphene: undoped
samples may exhibit collective excitations (in contrast to the equilibrium
situation), and the properties of the excitations in doped graphene are
strongly influenced by the ac field. We also show that the intensity of the
external field is the critical control parameter for the stability of these
excitations.
