Haag's Theorem in Noncommutative Quantum Field Theory

TL;DR

This paper extends Haag's theorem to noncommutative quantum field theory, demonstrating that the S-matrix's properties are preserved under certain transformations even when time and space do not commute.

Contribution

It generalizes Haag's theorem to noncommutative quantum field theories with SO(1,1) invariance, covering cases where time and space variables do not commute.

Findings

Haag's theorem holds in noncommutative QFT with noncommuting time and space.

The S-matrix being unity in one theory implies the same in related theories.

The result applies broadly to any SO(1,1) invariant quantum field theory.

Abstract

Haag's theorem was extended to noncommutative quantum field theory in a general case when time does not commute with spatial variables. It was proven that if S-matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in another theory is equal to unity as well. In fact this result is valid in any SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory.