Adiabatic theorem in axiomatic quantum field theory

Abstract

It is shown that Møller matricesS ± and scattering matrixS in axiomatic field theory can be expressed through their adiabatic analogs. In particular, it is proved under certain conditions that $$S_ - = \mathop {s\lim }\limits_{\alpha \to 0} S_\alpha (0,\infty )W_\alpha $$ whereW α is a trivial phase factor [i.e. a unitary operator of the form exp i / α ∝r(k)a + (k)a(k)dk]. Corresponding results in Hamiltonian approach are discussed.