alpha^star-Cohomology and Classification of Translation-Invariant Non-Commutative Quantum Field Theories

TL;DR

This paper explores alpha^star-cohomology to classify translation-invariant non-commutative quantum field theories, demonstrating that all quantum behaviors are fully characterized by these cohomology classes.

Contribution

It introduces a cohomological framework to classify and analyze translation-invariant non-commutative quantum field theories, linking quantum behaviors to alpha^star-cohomology classes.

Findings

Quantum behaviors are characterized by alpha^star-cohomology classes.

Green's functions and scattering matrices are determined by these cohomology classes.

The classification provides a complete understanding of translation-invariant non-commutative QFTs.

Abstract

Translation-invariant products are studied in the setting of alpha^star-cohomology. It is explicitly shown that all quantum behaviors including the Green's functions and the scattering matrix of translation-invariant non-commutative quantum field theories are thoroughly characterized by alpha^star-cohomology classes of the star products.