Haag's theorem in S O (1, k) invariant quantum field theory

TL;DR

This paper extends Haag's theorem to S O (1, k) invariant quantum field theories, including noncommutative cases, showing that equality of certain functions implies equality of scattering amplitudes and S-matrices.

Contribution

It generalizes Haag's theorem to higher-dimensional and noncommutative quantum field theories, revealing new implications for scattering processes and S-matrix properties.

Findings

Equality of four-point Wightman functions implies equality of scattering amplitudes.

In noncommutative QFT, S-matrix unity in one theory implies unity in another.

Generalized Haag's theorem applies to theories with additional coordinates, including noncommutative ones.

Abstract

Generalized Haag's theorem has been proved in S O (1, k) invariant quantum field theory. Apart from the above mentioned k+1 variables there can be arbitrary number of additional coordinates including noncommutative ones in the theory. New consequences of generalized Haag's theorem are obtained. It has been proved that the equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and thus the total cross-sections in these theories. In space-space noncommutative quantum field theory in four-dimensional case it has been proved that if in one of the theories under consideration S-matrix is equal to unity, then in another theory S-matrix is unity as well.