On the Question of the Scattering Matrix in Quantum Field Theory

Abstract

A new expression for the scattering matrix in local quantum field theory is obtained on the basis of a generalized formulation of the microcausality condition. This expression is relativistically covariant, unitary, and causal and coincides with the generally accepted expression (the T-exponential) in the case when ultraviolet (UV) divergences are absent in the latter. Conditions are formulated, under the fulfillment of which the elements of the constructed matrix do not contain UV divergences. By way of an example, the probability amplitude of the particle–particle transition for a model with ℒ(x) = λ : φ³(x): in the second-order perturbation theory is found.