In this book, the author presents the theory of quasifree quantum fields and argues that they could provide non-zero scattering for some particles. The free-field representation of the quantised transverse electromagnetic field is not closed in the weak*-topology. Its closure contains soliton–anti-soliton pairs as limits of two-photon states as time goes to infinity, and the overlap probability can be computed using Uhlmann's prescription. There are no free parameters: the probability is determined with no requirement to specify any coupling constant. All cases of the Shale transforms of the free field ϕ of the form ϕ→ϕ+φ, where φ is not in the one-particle space, are treated in the book. There remain the cases of the Shale transforms of the form ϕ → Tϕ, where T is a symplectic map on the one-particle space, not near the identity.