Local Scattering Operators for P(\phi)_2 Models and the Time-dependent Schr\"odinger Equation

TL;DR

This paper proves the existence of local scattering operators in P(φ)_2 quantum field models using evolution semigroups to address the well-posedness of the time-dependent Schrödinger equation.

Contribution

It introduces a nonperturbative method for establishing local scattering operators in quantum field theory models via evolution semigroups.

Findings

Existence of Bogoliubov's local scattering operators for P(φ)_2 models.

New well-posedness results for the time-dependent Schrödinger equation.

Application of evolution semigroups to quantum field theory problems.

Abstract

We establish the existence of Bogoliubov's local scattering operators for P(\phi)_2 models of constructive quantum field theory in a nonperturbative way. To this end, we use the technique of evolution semigroups to prove a new result on wellposedness of the Cauchy problem for the time-dependent Schr\"odinger equation under very general assumptions.