Generalized Haag's Theorem in SO(1,1) and SO(1,3) Invariant Quantum Field Theory

TL;DR

This paper proves a generalized Haag's theorem for SO(1,1) invariant quantum field theory, including noncommutative cases, and explores its implications for SO(1,3) invariant theories, linking Wightman functions to scattering amplitudes.

Contribution

It extends the generalized Haag's theorem to SO(1,1) invariant QFT and derives new consequences for SO(1,3) invariant theories, connecting correlation functions to scattering data.

Findings

Proved generalized Haag's theorem in SO(1,1) invariant QFT.

Established that equality of four-point Wightman functions implies identical scattering amplitudes.

Linked correlation functions to observable scattering quantities in SO(1,3) invariant theories.

Abstract

One of the most important results of the axiomatic quantum field theory - generalized Haag's theorem - is proven in SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In SO(1,3) invariant theory new consequences of generalized Haag's theorem are obtained: it has been proved that equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and total cross-sections in these theories.