Oscillon Floquet Modes and the Operators that Excite Them

We present the scattering modes of the oscillon, to the first three orders in the Fodor expansion, in terms of elementary functions. In the case of relativistic modes, these results are new. We use them to fully decompose the field and also to analytically invert the decomposition. In quantum field theory, this allows us to show that the corresponding creation and annihilation operators satisfy the usual oscillator algebra, extending to relativistic modes the demonstration that, at a fixed order in the Fodor expansion, a periodic oscillon state exists.