Another Convergent, Relativistic Model Theory of Interacting Particles : A Relativistic Version of a Modified Lee Model

概要

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The existence of a unitary representation of the inhomogeneous Lorentz group, which corresponds to a relativistic version of a modified Lee model, is proved through the process of actual construction of a set of ten generators (P_μ, M_<μν>) in terms of creation- and annihilation-operators of three kinds of particles. The model theory contains ab initio a cutoff form factor which is kept, throughout the whole scheme of the formalism, as it stands. The cutoff form factor is a function only of the invariant square of momentum transfer at the primary interaction vertex. By virtue of the cutoff form factor the theory has no divergence difficulties. The total Hamiltonian, H(≡-iP_4), of the model contains, from the very beginning and in an inevitable way, a finite "mass-renormalization term". The inclusion of that term in the Hamiltonian is inevitable in order for the ten generators to satisfy the set of fundamental commutator equations. Thus it turns out that the "mass-renormalization term" subtly takes its proper place within the realm of the formalism.
理論物理学刊行会の論文
1968-05-25