Existence of the Bogoliubov S(g) operator for the $(:{\varphi }^4:{)}_2$ quantum field theory

Abstract

We prove the existence of the Bogoliubov S(g) operator for the $(:{\varphi }^4:{)}_2$ quantum field theory for coupling functions $g$ of compact support in space and time. The construction is nonperturbative and relies on a theorem of Kisyński. It implies almost automatically the properties of unitarity and causality for disjoint supports in the time variable.

LaTeX, 24 pages, minor modifications, typos corrected

References in corpus (2)

• A local (perturbative) construction of observables in gauge theories: the example of QED
• Converging Perturbative Solutions of the Schroedinger Equation for a Two-Level System with a Hamiltonian Depending Periodically on Time

Cited by in corpus (1)

• A C*-algebraic approach to interacting quantum field theories