Abstract: In this book, we have briefly studied quasifree quantum fields, and argued that they could provide non-zero scattering for some particles. This is surprising, since by definition, a quasifree quantum field is one with zero as the value of any connected time-ordered product of n quantised fields. We start with the Wightman functions of the free tranverse electromagnetic fields, and construct the C*-algebra 
of the Fock representation. We note that the algebra 
has some non-Fock representations. Some states in the Fock representation converge as time goes to infinity to states which are not in Fock space, but can be interpreted as products of a specific non-Fock pair of a particle and its antiparticle. The convergence is in the weak* topology, and the states are normalised positive linear forms on our C*-algebra 
. At infinite time, these lie in an inequivalent representation, possibly reducible. For all finite times, the free photon system is in a state which has a non-zero scalar product with some reducible exponential states on our algebra; these can be represented as an infinite sum of vacuum, one-photon states, two-photon states, and so on. Each n-photon state lies in Fock space, but the norm of the sum is infinite. The theory thus gives a prediction, for example, of the probability that two photons will produce the compound state being considered: it is the square of the two-photon contribution to the compound. The interesting fact is that there is no freedom to choose the effective coupling constant: it is uniquely determined by the theory. If we make the conjecture, that there do not exist Wightman theories that are not quasifree in four space-time dimensions, then it would follow that all types of particles might be produced by examining such models…
