Regular Perturbation and Asymptotic Limits of Operators in Quantum Field Theory

Abstract

In the framework of the theory of regular perturbation asymptotic operators in quantum field theory are defined by means of a strong convergence in the Hilbert space, The fixed source theory and the boson-fermion system with extended interaction are particularly concerned. It is proved that .. adjusted annihilation and creation operators satisfy the equations of motion in differential as well as in integral forms and tend, at remote times, toward their asymptotic limits which have the same physical contents required in the axi­ omatic quantum field theory. It is also shown that the commutation relations between these asymptotic operators and the total Hamiltonian are of the same form as those between free operators and the free Hamiltonian. This gives us some definite information on the spectrum of the total Hamiltonian. As an example Lee's Hamiltonian with recoils is analyzed.